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Mat. Sb., 1998, Volume 189, Number 1, Pages 21–44 (Mi msb288)  

This article is cited in 13 scientific papers (total in 13 papers)

Self-dual geometry of generalized Hermitian surfaces

O. E. Arsen'eva, V. F. Kirichenko

Moscow State Pedagogical University

Abstract: Several results on the geometry of conformally semiflat Hermitian surfaces of both classical and hyperbolic types (generalized Hermitian surfaces) are obtained. Some of these results are generalizations and clarifications of already known results in this direction due to Koda, Itoh, and other authors. They reveal some unexpected beautiful connections between such classical characteristics of conformally semiflat (generalized) Hermitian surfaces as the Einstein property, the constancy of the holomorphic sectional curvature, and so on. A complete classification of compact self-dual Hermitian $RK$-surfaces that are at the same time generalized Hopf manifolds is obtained. This provides a complete solution of the Chen problem in this class of Hermitian surfaces.

DOI: https://doi.org/10.4213/sm288

Full text: PDF file (335 kB)
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English version:
Sbornik: Mathematics, 1998, 189:1, 19–41

Bibliographic databases:

UDC: 514.76
MSC: 53C55, 53B35
Received: 16.12.1996

Citation: O. E. Arsen'eva, V. F. Kirichenko, “Self-dual geometry of generalized Hermitian surfaces”, Mat. Sb., 189:1 (1998), 21–44; Sb. Math., 189:1 (1998), 19–41

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. F. Kirichenko, L. I. Vlasova, “Concircular geometry of nearly Kähler manifolds”, Sb. Math., 193:5 (2002), 685–707  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. M. B. Banaru, “O tipovom chisle slabo kosimplekticheskikh giperpoverkhnostei priblizhenno kelerovykh mnogoobrazii”, Fundament. i prikl. matem., 8:2 (2002), 357–364  mathnet  mathscinet  zmath
    3. M. B. Banaru, “Ob ermitovykh mnogoobraziyakh, udovletvoryayuschikh aksiome $U$-kosimplekticheskikh giperpoverkhnostei”, Fundament. i prikl. matem., 8:3 (2002), 943–947  mathnet  mathscinet  zmath
    4. M. B. Banaru, “The type number of the cosymplectic hypersurfaces of 6-dimensional Hermitian submanifolds of the Cayley algebra”, Siberian Math. J., 44:5 (2003), 765–773  mathnet  crossref  mathscinet  zmath  isi
    5. M. B. Banaru, “On skew-symplectic hypersurfaces of six-dimensional Kählerian submanifolds of the Cayley algebra”, Russian Math. (Iz. VUZ), 47:7 (2003), 60–63  mathnet  mathscinet  zmath  elib
    6. M. B. Banaru, “On Sasakian hypersurfaces in 6-dimensional Hermitian submanifolds of the Cayley algebra”, Sb. Math., 194:8 (2003), 1125–1136  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. M. B. Banaru, “On the Kenmotsu hypersurfaces of special Hermitian manifolds”, Siberian Math. J., 45:1 (2004), 7–10  mathnet  crossref  mathscinet  zmath  isi  elib
    8. V. F. Kirichenko, “Generalized Gray–Hervella classes and holomorphically projective transformations of generalized almost-Hermitian structures”, Izv. Math., 69:5 (2005), 963–987  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. D. V. Alekseevsky, C. Medori, A. Tomassini, “Homogeneous para-Kähler Einstein manifolds”, Russian Math. Surveys, 64:1 (2009), 1–43  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. A. V. Aristarkhova, “Pseudoconformally-flat and pseudo-flat quasi-Sasakian manifolds”, Russian Math. (Iz. VUZ), 53:12 (2009), 59–62  mathnet  crossref  mathscinet  zmath  elib
    11. Aristarkhova A.V., “O kontaktno konformno poluploskikh mnogoobraziyakh Kenmotsu”, Sovremennye naukoemkie tekhnologii, 2009, no. 6, 6–7  elib
    12. A. V. Aristarkhova, V. F. Kirichenko, “Contact Self-Dual Geometry of Quasi-Sasakian 5-Manifolds”, Math. Notes, 90:5 (2011), 625–638  mathnet  crossref  crossref  mathscinet  isi
    13. Abood H.M., Abdulameer Ya.A., “Vaisman-Gray Manifold of Pointwise Holomorphic Sectional Conharmonic Tensor”, Kyungpook Math. J., 58:4 (2018), 789–799  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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