$i$-convexity of manifolds with real projective structures
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- by Suhyoung Choi PDF
- Proc. Amer. Math. Soc. 122 (1994), 545-548 Request permission
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 ${{\mathbf {S}}^n}$.References
- Yves Carrière, Autour de la conjecture de L. Markus sur les variétés affines, Invent. Math. 95 (1989), no. 3, 615–628 (French, with English summary). MR 979369, DOI 10.1007/BF01393894 S. Choi, Convex decompositions of real projective surfaces I: $\pi$-annuli and convexity (to appear).
- Dennis Sullivan and William Thurston, Manifolds with canonical coordinate charts: some examples, Enseign. Math. (2) 29 (1983), no. 1-2, 15–25. MR 702731
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 545-548
- MSC: Primary 57M50; Secondary 53C10
- DOI: https://doi.org/10.1090/S0002-9939-1994-1197533-7
- MathSciNet review: 1197533