Nikonorov, Yurii Gennadyevich

Total publications: 80 (80)
in MathSciNet: 74 (74)
in zbMATH: 61 (61)
in Web of Science: 45 (45)
in Scopus: 54 (54)
Cited articles: 72
Citations in Math-Net.Ru: 188
Citations in Web of Science: 258
Citations in Scopus: 344

Number of views:
This page:6076
Abstract pages:8955
Full texts:2411
Nikonorov, Yurii Gennadyevich
Doctor of physico-mathematical sciences (2004)
Speciality: 01.01.04 (Geometry and topology)
Birth date: 6.05.1971
Keywords: integral mean value theorems, integral inequalities with deviating argument, convex geometry, differential geometry, global Riemannian geometry, homogeneous spaces, Einstein homogeneous manifolds, geodesic orbit spaces, Killing vector fields of constant length.
UDC: 511.26, 512.812, 513, 514, 514.74, 514.752.7, 514.76, 514.765, 515.143, 515.143.28, 517, 517.26, 517.383, 517.98, 514.752.22
MSC: 52A, 52B, 53C25, 53C30, 26A24


A positive solution of V. K. Ionin's conjecture was obtained. Namely, let $f$ be a continuous real-valued function defined on the segment $[0,1]$. For all $x\in(0,1]$, consider a value $\xi(x)$ that is the maximum of $\tau\in[0,x]$ with the property $xf(\tau)=\int_0^xf(t)\,dt$. Then $\varlimsup_{x\to 0}\frac{\xi(x)}{x}\ge\frac{1}{e}$. Some generalizations of this result are obtained (particularly, in a joint paper with V. V. Ivanov). Some problems of convex geometry are solved. New examples of Einstein homogeneous metrics are found with using various methods. Compact seven-dimensional and non-compact five-dimensional homogeneous Einstein manifolds are classified. The classes of $\delta$-homogeneous and Clifford-Wolf homogeneous Riemannian manifolds are studied, in particular, the classification of simply connected Clifford-Wolf homogeneous Riemannian manifolds is obtained (joint with V. N. Berestovskii). The structure of geodesic orbit Riemannian spaces is studied. The classification of simply connected compact geodesic orbit spaces of positive Euler characteristic is obtained (joint with D. V. Alekseevsky). The classification of generalized Wallach spaces is obtained. The structure of Killing vector fields of constant length on compact homogeneous Riemennian manifolds is studied.


Graduated from Faculty of Mathematics and Mechanics of Novosibirsk State University (NSU) in 1993 (department of mathematical analysis). Ph. D. thesis was defended in 1995, Doctor of Science thesis was defended in 2004. The list of my publications contains more than 70 titles.

Main publications:
  1. Ivanov V. V., Nikonorov Yu. G., “Asymptotic behavior of the Lagrange points in the Taylor formula”, Siberian Math. J., 36:1 (1995), 78–83  crossref  mathscinet  zmath  isi
  2. Nikonorov Yu. G., “Compact homogeneous Einstein 7-manifolds”, Geom. Dedicata, 109 (2004), 7–30  crossref  mathscinet  zmath  isi
  3. Nikonorov Yu. G., “Noncompact homogeneous Einstein 5-manifolds”, Geom. Dedicata, 113:1 (2005), 107–143  crossref  mathscinet  zmath  isi
  4. Berestovskii V. N., Nikonorov Yu. G., “On $\delta$-homogeneous Riemannian manifolds”, Differential Geom. Appl., 26:5 (2008), 514–535  crossref  mathscinet  zmath  isi
  5. Berestovskii V. N., Nikonorov Yu. G., “Clifford-Wolf homogeneous Riemannian manifolds”, J. Differ. Geometry, 82:3 (2009), 467–500  mathscinet  zmath  isi
List of publications on Google Scholar

Full list of publications:
| by years | by types | by times cited in WoS | by times cited in Scopus | scientific publications | common list |

1. Z. Chen, Yu. G. Nikonorov, “Invariant Einstein metrics on generalized Wallach spaces”, Science China Mathematics, 62:3 (2019), 569–584  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 3)
2. Y. Nikolayevsky, Yu. G. Nikonorov, “On invariant Riemannian metrics on Ledger–Obata spaces”, Manuscripta Mathematica, 158:3–4 (2019), 353–370  crossref  mathscinet  zmath  isi  scopus (cited: 1)
3. V. N. Berestovskii, Yu. G. Nikonorov, “On homogeneous geodesics and weakly symmetric spaces”, Ann. Glob. Anal. Geom., 55:3 (2019), 575–589  crossref  isi (cited: 6)  scopus (cited: 7)
4. Yu. G. Nikonorov, “On left-invariant Einstein Riemannian metrics that are not geodesic orbit”, Transform. Groups, 24:2 (2019), 511–530  crossref  isi (cited: 1)  scopus (cited: 1)

5. C. S. Gordon, Yu. G. Nikonorov, “Geodesic orbit Riemannian structures on $\mathbb{R}^n$”, Journal of Geometry and Physics, 134 (2018), 235–243  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  scopus (cited: 3)

6. Z. Chen, Yu. G. Nikonorov, Yu. V. Nikonorova, “Invariant Einstein metrics on Ledger–Obata spaces”, Differential Geometry and its Applications, 50 (2017), 71–87  crossref  mathscinet  zmath  isi (cited: 4)  scopus (cited: 6)
7. Yu. G. Nikonorov, “On the structure of geodesic orbit Riemannian spaces”, Ann. Glob. Anal. Geom., 52:3 (2017), 289–311  crossref  zmath  isi (cited: 5)  scopus (cited: 6)

8. Yu. G. Nikonorov, “Classification of generalized Wallach spaces”, Geometriae Dedicata, 181:1 (2016), 193–212  crossref  mathscinet  zmath  isi (cited: 9)  scopus (cited: 12)
9. N. A. Abiev, Yu. G. Nikonorov, “The evolution of positively curved invariant Riemannian metrics on the Wallach spaces under the Ricci flow”, Ann. Glob. Anal. Geom., 50:1 (2016), 65–84  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 5)

10. Y. Nikolayevsky, Yu. G. Nikonorov, “On solvable Lie group of negative Ricci curvature”, Mathematische Zeitschrift, 280:1–2 (2015), 1–16  crossref  mathscinet  zmath  isi (cited: 3)  scopus (cited: 6)
11. Yu. G. Nikonorov, “Killing vector fields of constant length on compact homogeneous Riemannian manifolds”, Ann. Glob. Anal. Geom., 48:4 (2015), 305–330  crossref  mathscinet  zmath  isi (cited: 1)  elib (cited: 1)  scopus (cited: 2)
12. Yu. G. Nikonorov, Asymptotics of the mean value points, SMI VSC RAS, Vladikavkaz, 2015 , 200 pp.  elib

13. V. N. Berestovskii, Yu. G. Nikonorov, “Generalized normal homogeneous Riemannian metrics on spheres and projective spaces”, Ann. Glob. Anal. Geom., 45:3 (2014), 167–196  crossref  mathscinet  zmath  isi (cited: 6)  elib (cited: 2)  scopus (cited: 7)

14. Yu. G. Nikonorov, “Asymptotics of mean value points in the Schwarz theorem for divided differences”, Siberian Adv. Math., 25:1 (2015), 56–75  mathnet  crossref  mathscinet  zmath  elib  elib  scopus

15. Yu. G. Nikonorov, “Negative eigenvalues of the Ricci operator of solvable metric Lie algebras”, Geometriae Dedicata, 170:1 (2014), 119–133  crossref  mathscinet  zmath  isi (cited: 2)  elib (cited: 1)  scopus (cited: 2)
16. N. A. Abiev, A. Arvanitoyeorgos, Yu. G. Nikonorov, P. Siasos, “The dynamics of the Ricci flow on generalized Wallach spaces”, Differential Geometry and its Applications, 35:Supplement (2014), 26–43  crossref  mathscinet  zmath  isi (cited: 8)  scopus (cited: 10)
17. N. A. Abiev, A. Arvanitoyeorgos, Yu. G. Nikonorov, P. Siasos, “The Ricci flow on some generalized Wallach spaces”, Geometry and its Applications, Springer Proceedings in Mathematics & Statistics, Vol. 72, eds. V. Rovenski, P. Walczak, Springer, 2014, 3–37  crossref  mathscinet  zmath  scopus (cited: 7)
18. N. V. Abrosimov, E. Makai, Jr., A. D. Mednih, Yu. G. Nikonorov, G. Rote, “The infinum of the volumes of convex polytops of any given facet areas is $0$”, Studia Scientiarum Mathematicarum Hungarica, 51:4 (2014), 466–519  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus (cited: 1)

19. Yu. G. Nikonorov, “Peano's theorem and coplanarity points of space curves”, Siberian Adv. Math., 25, No 2, 124–137 (2015), Siberian Adv. Math., 25:2 (2015), 124–137  mathnet  crossref  mathscinet  elib  elib  scopus

20. Yu. G. Nikonorov, “Killing vector fields and the curvature tensor of a Riemannian manifold”, Siberian Adv. Math., 24:3 (2014), 187–192  mathnet  crossref  mathscinet  zmath  elib  elib  scopus

21. Yu. G. Nikonorov, “Geodesic orbit manifolds and Killing fields of constant length”, Hiroshima Math. J., 43:1 (2013), 129–137 Project Euclid  mathscinet  zmath  isi (cited: 7)  elib (cited: 1)  scopus (cited: 7)
22. Yu. G. Nikonorov, “Geodesic orbit Riemannian metrics on spheres”, Vladikavkaz. Mat. Zh., 15:3 (2013), 67-76  mathnet (cited: 2)  zmath  elib

23. Yu. G. Nikonorov, “Asymptotic behavior of support points for planar curves”, J. Math. Anal. Appl., 391:1 (2012), 147–158  crossref  mathscinet  zmath  isi  elib (cited: 8)  scopus (cited: 2)

24. Yu. G. Nikonorov, “Double exponential map on symmetric spaces”, Siberian Adv. Math., 23:3 (2013), 210–218  mathnet  crossref  mathscinet  elib  elib  scopus

25. V. N. Berestovskii, Yu. G. Nikonorov, Riemannian manifolds and homogeneous geodesics, SMI VSC RAS, Vladikavkaz, 2012 , 414 pp.  mathscinet  zmath

26. Yu. G. Nikonorov, M. S. Chebarykov, “The Ricci operator of completely solvable metric Lie algebras”, Siberian Adv. Math., 24:1 (2014), 18–25  mathnet  crossref  mathscinet  elib  elib  scopus

27. Yu. G. Nikonorov, “Asymptotics of tangent points for planar curves”, Siberian Adv. Math., 22:3 (2012), 192–203  mathnet  crossref  mathscinet  elib  elib  scopus

28. V. N. Berestovskii, E. V. Nikitenko, Yu. G. Nikonorov, “Classification of generalized normal homogeneous Riemannian manifolds of positive Euler characteristic”, Differential Geometry and its Applications, 29:4 (2011), 533–546  crossref  mathscinet  zmath  isi (cited: 5)  scopus (cited: 6)
29. Yu. G. Nikonorov, Yu. V. Nikonorova, “On an approach to the solution of the J. W. Fickett problem of overlapping congruent polygons”, Vladikavkaz. Mat. Zh., 13:4 (2011), 52–59  mathnet  mathscinet  elib

30. A. G. Kremlyov, Yu. G. Nikonorov, “The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The nonunimodular case”, Siberian Adv. Math., 20:1 (2010), 1–57  mathnet  crossref  mathscinet  elib (cited: 4)  elib (cited: 4)  scopus (cited: 6)

31. Dmitrii V. Alekseevsky, Yurii G. Nikonorov, “Compact Riemannian Manifolds with Homogeneous Geodesics”, SIGMA, 5 (2009), 93–16  mathnet (cited: 21)  crossref  mathscinet  isi (cited: 20)  scopus (cited: 20)
32. V. N. Berestovskii, Yu. G. Nikonorov, “On $\delta$-homogeneous Riemannian manifolds. II”, Siberian Math. J., 50:2 (2009), 214–222  mathnet  crossref  mathscinet  zmath  isi (cited: 7)  elib (cited: 10)  elib (cited: 10)  scopus (cited: 9)
33. V. N. Berestovskii, Yu. G. Nikonorov, “Clifford-Wolf homogeneous Riemannian manifolds”, Journal of Differential Geometry, 82:3 (2009), 467–500 Project Euclid  mathscinet  zmath  isi (cited: 23)  scopus (cited: 27)
34. A. Arvanitoyeorgos, V. V. Dzhepko, Yu. G. Nikonorov, “Invariant Einstein metrics on some homogeneous spaces of classical Lie groups”, Canadian Journal of Mathematics, 61:6 (2009), 1201–1213  crossref  mathscinet  zmath  isi (cited: 10)  scopus (cited: 11)
35. A. G. Kremlyov, Yu. G. Nikonorov, “The Signature of the Ricci Curvature of Left-Invariant Riemannian Metrics on Four-Dimensional Lie Groups. The Unimodular Case”, Siberian Adv. Math., 19:4 (2009), 245–267  mathnet  crossref  mathscinet  elib (cited: 3)  elib (cited: 3)  scopus (cited: 6)

36. V. N. Berestovskii, Yu. G. Nikonorov, “Killing vector fields of constant length on Riemannian manifolds”, Siberian Math. J., 49:3 (2008), 395–407  mathnet  crossref  mathscinet  zmath  isi (cited: 22)  elib (cited: 15)  elib (cited: 15)  scopus (cited: 26)
37. V. N. Berestovskii, Yu. G. Nikonorov, “On $\delta$-homogeneous Riemannian manifolds”, Differential Geometry and its Applications, 26:5 (2008), 514–535  crossref  mathscinet  isi (cited: 22)  scopus (cited: 24)
38. Yu. G. Nikonorov, Yu. V. Nikonorova, “The intrinsic diameter of the surface of a parallelepiped”, Discrete and Computational Geometry, 40:4 (2008), 504–527  crossref  mathscinet  zmath  isi (cited: 3)  scopus (cited: 4)
39. A. Arvanitoyeorgos, V. V. Dzhepko, Yu. G. Nikonorov, “Invariant Einstein metrics on certain Stiefel manifolds”, Kowalski, Oldrich (ed.) et al., Differential geometry and its applications. Proceedings of the 10th international conference on differential geometry and its applications, DGA 2007 (Olomouc, Czech Republic, August 27–31, 2007), World Scientific, Hackensack, NJ, 2008, 35–44  mathscinet  zmath
40. V. V. Balaschenko, Yu. G. Nikonorov, E. D. Rodionov, V. V. Slavskii, Odnorodnye prostranstva: teoriya i prilozheniya, Poligrafist, Khanty-Mansiisk, 2008 , 280 pp.
41. V. N. Berestovskii, Yu. G. Nikonorov, “Killing vector fields of constant length on locally symmetric Riemannian manifolds”, Transform. Groups, 13:1 (2008), 25–45  crossref  mathscinet  zmath  isi (cited: 17)  elib (cited: 14)  scopus (cited: 16)

42. V. N. Berestovskii, Yu. G. Nikonorov, “The Chebyshev norm on the Lie algebra of the motion group of a compact homogeneous Finsler manifold”, Journal of Mathematical Sciences (New York), 161:1 (2009), 97–121  crossref  mathscinet  zmath  scopus (cited: 3)

43. V. N. Berestovskii, Yu. G. Nikonorov, “On Clifford-Wolf homogeneous Riemannian manifolds”, Doklady Mathematics, 78:3 (2008), 807–810  mathnet  crossref  mathscinet  zmath  isi (cited: 4)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 3)
44. V. N. Berestovskii, Yu. G. Nikonorov, “Regular and Quasiregular Isometric Flows on Riemannian Manifolds”, Siberian Adv. Math., 18:3 (2008), 153–162  mathnet  crossref  mathscinet  elib (cited: 2)  elib (cited: 2)  scopus (cited: 2)

45. Yu. G. Nikonorov, “On Einstein Extensions of Nilpotent Metric Lie Algebras”, Siberian Adv. Math., 17:3 (2007), 153–170  mathnet  crossref  mathscinet  elib

46. V. V. Dzhepko, Yu. G. Nikonorov, “The Double Exponential Map on Spaces of Constant Curvature”, Siberian Adv. Math., 18:1 (2008), 21–29  mathnet  crossref  mathscinet  elib  elib  scopus

47. V. N. Berestovskii, Yu. G. Nikonorov, “Continued Fractions, the Group $\mathrm{GL}(2,\mathbb Z)$, and Pisot Numbers”, Siberian Adv. Math., 17:4 (2007), 268–290  mathnet  crossref  mathscinet  elib
48. E. V. Volnikh, A. V. Kutishkin, Yu. G. Nikonorov, “Construction of the $\delta$-homogeneous VES production function”, Sib. Zh. Ind. Mat., 10:2 (2007), 31–44  mathnet  mathscinet  elib
49. A. Arvanitoyeorgos, V. V. Dzhepko, Yu. G. Nikonorov, “Invariant Einstein metrics on quaternionic Stiefel manifolds”, Bull. Greek Math. Soc., 53 (2007), 1–14  mathscinet  zmath
50. V. N. Berestovskii, Yu. G. Nikonorov, “On $\delta $-homogeneous Riemannian manifolds”, Doklady Mathematics, 76:1 (2007), 596–598  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 3)
51. Yu. G. Nikonorov, E. D. Rodionov, V. V. Slavskii, “Geometry of homogeneous Riemannian manifolds”, Journal of Mathematical Sciences (New York), 146:7 (2007), 6313–6390  crossref  mathscinet  zmath  scopus (cited: 31)

52. E. V. Nikitenko, Yu. G. Nikonorov, “Six-Dimensional Einstein Solvmanifolds”, Siberian Adv. Math., 16:1 (2006), 66–112  mathnet  mathscinet  elib

53. Yu. G. Nikonorov, “Noncompact homogeneous Einstein 5-manifolds”, Geometriae Dedicata, 113:1 (2005), 107–143  crossref  mathscinet  zmath  isi (cited: 13)  elib (cited: 11)  scopus (cited: 11)

54. Yu. G. Nikonorov, “Compact homogeneous Einstein 7-manifolds”, Geometriae Dedicata, 109:1 (2004), 7–30  crossref  mathscinet  zmath  isi (cited: 13)  scopus (cited: 14)
55. A. M. Lomshakov, Yu. G. Nikonorov, E. V. Firsov, “Invariant Einstein Metrics on Three-Locally-Symmetric Spaces”, Siberian Adv. Math., 14:3 (2004), 43–62  mathnet  mathscinet  zmath  elib
56. D. V. Vasin, Yu. G. Nikonorov, “A Problem of L. Fejes Tóth in a Multidimensional Euclidean Space”, Siberian Adv. Math., 14:2 (2004), 116–125  mathnet  mathscinet  zmath  elib

57. Yu. G. Nikonorov, E. D. Rodionov, “Compact homogeneous Einstein 6-manifolds”, Differential Geometry and its Applications, 19:3 (2003), 369–378  crossref  mathscinet  zmath  isi (cited: 14)  scopus (cited: 16)
58. Yu. G. Nikonorov, “Invariant Einstein metrics on the Ledger–Obata spaces”, St. Petersburg Math. J., 14:3 (2003), 487–497  mathnet  mathscinet  zmath

59. Yu. G. Nikonorov, N. V. Rasskazova, “A Problem of Fejes L. Tóth”, Siberian Adv. Math., 12:4 (2002), 34–43  mathnet  mathscinet  zmath  elib
60. Yu. G. Nikonorov, “On the asymptotics of mean value points for some finite-difference operators”, Siberian Math. J., 43:3 (2002), 518–524  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 3)
61. E. V. Lomshakov, Yu. G. Nikonorov, E. V. Firsov, “On invariant Einstein metrics on three-locally-symmetric spaces”, Doklady Mathematics, 66:2 (2002), 224–227  mathnet  mathscinet  zmath  isi (cited: 1)  scopus

62. Yu. G. Nikonorov, “On the asymptotic of the mean value points for some finite difference operators”, Fundam. Prikl. Mat., 7:3 (2001), 829–838  mathnet  mathscinet  zmath
63. Yu. G. Nikonorov, “Compact Homogeneous Einstein 7-Manifolds”, Siberian Adv. Math., 11:1 (2001), 84–99  mathnet  mathscinet  zmath

64. Yu. G. Nikonorov, “Algebraic Structure of Standard Homogeneous Einstein Manifolds”, Siberian Adv. Math., 10:3 (2000), 59–82  mathnet  mathscinet  zmath
65. Yu. G. Nikonorov, “Tessellations of many-dimensional parallelepipeds”, Siberian Math. J., 41:4 (2000), 760–762  mathnet  crossref  mathscinet  zmath  isi
66. Yu. G. Nikonorov, “On the Ricci curvature of homogeneous metrics on noncompact homogeneous spaces”, Siberian Math. J., 41:2 (2000), 329–346  mathnet  crossref  mathscinet  zmath  isi (cited: 5)
67. Yu. G. Nikonorov, “On a class of homogeneous compact Einstein manifolds”, Siberian Math. J., 41:1 (2000), 168–172  mathnet  crossref  mathscinet  zmath  isi (cited: 9)
68. Yu. G. Nikonorov, “New series of Einstein homogeneous metrics”, Differential Geometry and its Applications, 12:1 (2000), 25–34  crossref  mathscinet  zmath  isi
69. Yu. G. Nikonorov, “On homogeneous Einstein manifolds”, Doklady Mathematics, 61:3 (2000), 328–331  mathnet  mathscinet  zmath  isi  scopus
70. Yu. G. Nikonorov, “On compact seven-dimensional homogeneous Einstein manifolds”, Doklady Mathematics, 61:3 (2000), 403–405  mathnet  mathscinet  zmath  isi  scopus

71. Yu. G. Nikonorov, “On Two Problems of Convex Geometry”, Siberian Adv. Math., 9:4 (1999), 59–65  mathnet  mathscinet  zmath
72. Yu. G. Nikonorov, E. D. Rodionov, “Six-dimensional compact homogeneous Einstein manifolds”, Doklady Mathematics, 59:3 (1999), 451–453  mathnet  mathscinet  zmath  scopus  scopus

73. Yu. G. Nikonorov, “The scalar curvature functional and homogeneous Einstein metrics on Lie groups”, Siberian Math. J., 39:3 (1998), 504–509  mathnet  crossref  mathscinet  zmath  isi (cited: 4)

74. Yu. G. Nikonorov, “Inscribed balls and the Lyusternik–Shnirel'man category”, Siberian Math. J., 38:5 (1997), 957–959  mathnet  crossref  mathscinet  zmath  isi

75. Yu. G. Nikonorov, E. D. Rodionov, “Standard homogeneous Einstein manifolds and diophantine equations”, Archivum Mathematicum, 32:2 (1996), 123–136  mathscinet  zmath

76. V. V. Ivanov, Yu. G. Nikonorov, “Asymptotic behavior of the Lagrange points in the Taylor formula”, Siberian Math. J., 36:1 (1995), 78–83  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 4)

77. Yu. G. Nikonorov, “A homotopic analog of Helly's theorem and the existence of quasi-invariant points”, Siberian Math. J., 35:3 (1994), 577–579  mathnet  crossref  mathscinet  zmath  isi  scopus
78. Yu. G. Nikonorov, “On sharp estimates in the first mean value theorem”, Doklady Mathematics, 49:3 (1994), 493–496  mathnet  mathscinet  zmath

79. Yu. G. Nikonorov, “On the integral mean value theorem”, Siberian Math. J., 34:6 (1993), 1135–1137  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 7)
80. V. K. Ionin, Yu. G. Nikonorov, “An uncountable family of disjoint spatial continua in Euclidean space”, Siberian Math. J., 34:5 (1993), 848–851  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)

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