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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Group-quotients with positive sectional curvatures
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by Robert Geroch PDF
Proc. Amer. Math. Soc. 66 (1977), 321-326 Request permission

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
  • L. Berard-Bergery, Les variétés riemanniennes homogènes simplement connexes de dimension impaire à courbure strictement positive, J. Math. Pures Appl. (9) 55 (1976), no. 1, 47–67 (French). MR 417987
  • Barrett O’Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459–469. MR 200865
  • Hans Samelson, On curvature and characteristic of homogeneous spaces, Michigan Math. J. 5 (1958), 13–18. MR 103509
  • J. L. Synge, The first and second variations of the length-integral in Riemannian space, Proc. London Math. Soc. (2) 25 (1926), 247-264.
  • Nolan R. Wallach, Compact homogeneous Riemannian manifolds with strictly positive curvature, Ann. of Math. (2) 96 (1972), 277–295. MR 307122, DOI 10.2307/1970789
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • 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