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 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}).
