Closed Hypersurfaces in Riemannian Manifolds Whose Second Fundamental Form are of Constant Length

Abstract

Listen

Translate article

In [2], Ye had proved the existence of a family of constant mean curvature hypersurfaces in an m+1‐dimensional Riemannian manifold (Mm+1,g), which concentrate at a point p0 (which is required to be a nondegenerate critical point of the scalar curvature). Recently Mahmoudi [1] extended this result to the other curvatures (the r‐th mean curvature for 1≤r≤m). In this paper, using a similar idea, we show that there exist compact hypersurfaces whose second fundamental form are of constant length.