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Mat. Sb. (N.S.), 1972, Volume 89(131), Number 2(10), Pages 280–296 (Mi msb3232)  

This article is cited in 20 scientific papers (total in 20 papers)

Groups of conformal transformations of Riemannian spaces

D. V. Alekseevskii

Abstract: It is proved that if a Riemannian space $(M,g)$ of class $C^\infty$ has a connected group of conformal transformations which leaves no conformally given metric $e^\sigma_g$ invariant, then $(M,g)$ is globally conformal to a sphere $(S^n,g_0)$ or to Euclidean space $(E^n,g_0)$.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Sbornik, 1972, 18:2, 285–301

Bibliographic databases:

UDC: 513.766
MSC: Primary 57E30; Secondary 53C10, 53A30
Received: 13.09.1971

Citation: D. V. Alekseevskii, “Groups of conformal transformations of Riemannian spaces”, Mat. Sb. (N.S.), 89(131):2(10) (1972), 280–296; Math. USSR-Sb., 18:2 (1972), 285–301

Citation in format AMSBIB
\by D.~V.~Alekseevskii
\paper Groups of conformal transformations of Riemannian spaces
\jour Mat. Sb. (N.S.)
\yr 1972
\vol 89(131)
\issue 2(10)
\pages 280--296
\jour Math. USSR-Sb.
\yr 1972
\vol 18
\issue 2
\pages 285--301

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    This publication is cited in the following articles:
    1. D. V. Alekseevskii, “$S^n$$E^n$ – edinstvennye rimanovy prostranstva, dopuskayuschie suschestvennoe konformnoe preobrazovanie”, UMN, 28:5(173) (1973), 225–226  mathnet  mathscinet  zmath
    2. D. V. Alekseevskii, “On perfect actions of Lie groups”, Russian Math. Surveys, 34:1 (1979), 215–216  mathnet  crossref  mathscinet  zmath
    3. Boris Kimelfeld, “Homogeneous domains on flag manifolds”, Journal of Mathematical Analysis and Applications, 121:2 (1987), 506  crossref
    4. D. V. Alekseevskii, “Conformal mappings of $G$-structures”, Funct. Anal. Appl., 22:4 (1988), 311–313  mathnet  crossref  mathscinet  zmath  isi
    5. Jacqueline Ferrand, “Convergence and degeneracy of quasiconformal maps of Riemannian manifolds”, J. Anal. Math, 69:1 (1996), 1  crossref
    6. W Kühnel, “Conformal vector fields on pseudo-Riemannian spaces”, Differential Geometry and its Applications, 7:3 (1997), 237  crossref
    7. V. N. Berestovskii, “Similarly homogeneous locally complete spaces with an intrinsic metric”, Russian Math. (Iz. VUZ), 48:11 (2004), 1–19  mathnet  mathscinet  elib
    8. Kang-Tae Kim, Luigi Verdiani, “Complexn-dimensional manifolds with a realn 2-dimensional automorphism group”, J Geom Anal, 14:4 (2004), 701  crossref
    9. M. N. Podoksenov, “In a Transitive Group of Conformal Transformations, Any Normal Subgroup with Orbit of Dimension $k>1$ is Inessential”, Math. Notes, 82:2 (2007), 279–282  mathnet  crossref  crossref  mathscinet  isi  elib
    10. Matveev, VS, “Proof of the projective Lichnerowicz-Obata conjecture”, Journal of Differential Geometry, 75:3 (2007), 459  isi  elib
    11. A. ROD GOVER, FELIPE LEITNER, “A CLASS OF COMPACT Poincaré–Einstein MANIFOLDS: PROPERTIES AND CONSTRUCTION”, Commun. Contemp. Math, 12:04 (2010), 629  crossref
    12. Jesse Alt, “Essential Parabolic Structures and Their Infinitesimal Automorphisms”, SIGMA, 7 (2011), 039, 16 pp.  mathnet  crossref  mathscinet
    13. M. Lampe, “On the isotropy subalgebras of Lie algebras of conformal vector fields”, Journal of Geometry and Physics, 2011  crossref
    14. N. I. Zhukova, “Attractors and an analog of the Lichnérowicz conjecture for conformal foliations”, Siberian Math. J., 52:3 (2011), 436–450  mathnet  crossref  mathscinet  isi
    15. Charles Frances, “Local dynamics of conformal vector fields”, Geom Dedicata, 2011  crossref
    16. Stuart Armstrong, Felipe Leitner, “Decomposable conformal holonomy in Riemannian signature”, Math. Nachr, 2011, n/a  crossref
    17. N. I. Zhukova, “Global attractors of complete conformal foliations”, Sb. Math., 203:3 (2012), 380–405  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. Vladimir S Matveev, Marc Troyanov, “The Binet–Legendre Metric in Finsler Geometry”, Geom. Topol, 16:04 (2012), 2135  crossref
    19. Jae-Cheon Joo, Kang-Hyurk Lee, “Subconformal Yamabe Equation and Automorphism Groups of Almost CR Manifolds”, J Geom Anal, 2013  crossref
    20. Alekseevsky D., “Lorentzian Manifolds With Transitive Conformal Group”, Note Mat., 37:1, S (2017), 35–47  crossref  mathscinet  isi  scopus
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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