On Curvature Pinching for Submanifolds with Parallel Normalized Mean Curvature Vector

Juanru Gu () and Yao Lu
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Juanru Gu: Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China
Yao Lu: Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China

Mathematics, 2024, vol. 12, issue 11, 1-12

Abstract: In this note, we investigate the pinching problem for oriented compact submanifolds of dimension n with parallel normalized mean curvature vector in a space form F n + p ( c ) . We first prove a codimension reduction theorem for submanifolds under lower Ricci curvature bounds. Moreover, if the submanifolds have constant normalized scalar curvature R ≥ c , we obtain a classification theorem for submanifolds under lower Ricci curvature bounds. It should be emphasized that our Ricci pinching conditions are sharp for even n and p = 2 .

Keywords: submanifold; rigidity theorems; Ricci curvature; scalar curvature (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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