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

A sphere theorem for reverse volume pinching on even-dimensional manifolds


Authors: Leslie Coghlan and Yoe Itokawa
Journal: Proc. Amer. Math. Soc. 111 (1991), 815-819
MSC: Primary 53C20
MathSciNet review: 1042262
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Abstract: Let $ M$ be a compact simply connected riemannian manifold of even dimension $ d$. It is well known that if the sectional curvature of $ M$ lies in the range $ \left( {0,\lambda } \right]$, then $ M$ has volume greater than or equal to that of the $ d$-dimensional euclidean sphere $ S_\lambda ^d$ of constant curvature $ \lambda $. We prove that if the volume of $ M$ is no greater than 3/2 times that of $ S_\lambda ^d$, then $ M$ is homeomorphic with the sphere.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1042262-0
PII: S 0002-9939(1991)1042262-0
Article copyright: © Copyright 1991 American Mathematical Society