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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$ i$-convexity of manifolds with real projective structures


Author: Suhyoung Choi
Journal: Proc. Amer. Math. Soc. 122 (1994), 545-548
MSC: Primary 57M50; Secondary 53C10
MathSciNet review: 1197533
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Abstract: We compare the notion of higher-dimensional convexity, as defined by Carrière, for real projective manifolds with the existence of hemispheres. We show that if an i-convex real projective manifold M of dimension n for an integer i with $ 0 < i < n$ has an i-dimensional hemisphere, then M is projectively homeomorphic to $ {{\mathbf{S}}^n}/\Gamma $ where $ \Gamma $ is a finite subgroup of $ O(n + 1,{\mathbf{R}})$ acting freely on $ {{\mathbf{S}}^n}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1197533-7
PII: S 0002-9939(1994)1197533-7
Keywords: Convexity, generalization of convexity, projective geometry, geometric structures, real projective structures
Article copyright: © Copyright 1994 American Mathematical Society