Year: 1991
Type: article
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.
Authors: Leslie Coghlan, Yoe Itokawa
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2008108385