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Sbornik: Mathematics, 1995, Volume 186, Issue 7, Pages 941–950
DOI: https://doi.org/10.1070/SM1995v186n07ABEH000050
(Mi sm50)
 

This article is cited in 5 scientific papers (total in 5 papers)

Compact homogeneous manifolds with integrable invariant distributions, and scalar curvature

V. N. Berestovskii

Omsk State University
References:
Abstract: It is proved that for a compact simply-connected effective homogeneous space $G/H$ of a connected compact Lie group $G$ by a closed subgroup $H$ the following conditions are equivalent:
  • (1) Every $G$-invariant distribution on $G/H$ is integrable.
  • (2) The space $G/H$ is of normal type in the sense of Bergery.
  • (3) Every $G$-invariant Riemannian metric on $G/H$ has positive scalar curvature.
  • (4) The space $G/H$ is isomorphic to a direct product of compact simplyconnected strongly isotropy-irreducible homogeneous spaces.
Received: 10.05.1994
Russian version:
Matematicheskii Sbornik, 1995, Volume 186, Number 7, Pages 15–24
Bibliographic databases:
UDC: 514.747
MSC: Primary 53C30; Secondary 58A30
Language: English
Original paper language: Russian
Citation: V. N. Berestovskii, “Compact homogeneous manifolds with integrable invariant distributions, and scalar curvature”, Mat. Sb., 186:7 (1995), 15–24; Sb. Math., 186:7 (1995), 941–950
Citation in format AMSBIB
\Bibitem{Ber95}
\by V.~N.~Berestovskii
\paper Compact homogeneous manifolds with integrable invariant distributions, and scalar curvature
\jour Mat. Sb.
\yr 1995
\vol 186
\issue 7
\pages 15--24
\mathnet{http://mi.mathnet.ru/sm50}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1355453}
\zmath{https://zbmath.org/?q=an:0872.53033}
\transl
\jour Sb. Math.
\yr 1995
\vol 186
\issue 7
\pages 941--950
\crossref{https://doi.org/10.1070/SM1995v186n07ABEH000050}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TX11200002}
Linking options:
  • https://www.mathnet.ru/eng/sm50
  • https://doi.org/10.1070/SM1995v186n07ABEH000050
  • https://www.mathnet.ru/eng/sm/v186/i7/p15
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:307
    Russian version PDF:110
    English version PDF:19
    References:59
    First page:1
     
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