Hypersurfaces of Randers spaces with positive Ricci curvature
Volume 172 / 2023
Colloquium Mathematicum 172 (2023), 85-97
MSC: Primary 53C60; Secondary 53C40.
DOI: 10.4064/cm8535-4-2022
Published online: 26 October 2022
Abstract
Let $(\overline M^{n+1}, \overline F)$ be a Randers space with constant flag curvature $K=1$. We consider compact hypersurfaces $(M^n, F)$ of $(\overline M^{n+1}, \overline F)$ with constant mean curvature $|H|$. We prove that if the general Ricci curvature of $M$ is greater than or equal to $n-2$, then $M$ is either a Randers space with constant flag curvature $R=1+|H|^2$ or a Riemannian manifold isometric to $S^m(\sqrt {r})\times S^{n-m}(\sqrt {1-r^2})$.
