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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Group-quotients with positive sectional curvatures


Author: Robert Geroch
Journal: Proc. Amer. Math. Soc. 66 (1977), 321-326
MSC: Primary 53C20; Secondary 53C30
DOI: https://doi.org/10.1090/S0002-9939-1977-0464111-4
MathSciNet review: 0464111
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Abstract: Let H be a closed subgroup of compact Lie group G. A necessary and sufficient condition is obtained for the existence of a left-invariant Riemannian metric on G such that the subduced metric on the quotient H G has strictly positive sectional curvatures.


References [Enhancements On Off] (What's this?)

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  • [3] Hans Samelson, On curvature and characteristic of homogeneous spaces, Michigan Math. J. 5 (1958), 13–18. MR 0103509
  • [4] J. L. Synge, The first and second variations of the length-integral in Riemannian space, Proc. London Math. Soc. (2) 25 (1926), 247-264.
  • [5] Nolan R. Wallach, Compact homogeneous Riemannian manifolds with strictly positive curvature, Ann. of Math. (2) 96 (1972), 277–295. MR 0307122, https://doi.org/10.2307/1970789

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DOI: https://doi.org/10.1090/S0002-9939-1977-0464111-4
Article copyright: © Copyright 1977 American Mathematical Society