Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C20

Retrieve articles in all journals with MSC: 53C20

Additional Information

PII: S 0002-9939(1991)1042262-0
Article copyright: © Copyright 1991 American Mathematical Society