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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
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.

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  • 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
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Article copyright: © Copyright 1977 American Mathematical Society