Curvature Pinching Problems for Compact Pseudo-Umbilical PMC Submanifolds in S m ( c ) × R

Wang-Hua Qiu and Xin Zhan ()
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Wang-Hua Qiu: College of Sciences, Jiujiang University, Jiujiang 332005, China
Xin Zhan: School of Mathematics and Statistics, Changshu Institute of Technology, Suzhou 215500, China

Mathematics, 2023, vol. 12, issue 1, 1-15

Abstract: Let S m ( c ) denote a sphere with a positive constant curvature c and M n ( n ≥ 3 ) be an n -dimensional compact pseudo-umbilical submanifold in a Riemannian product space S m ( c ) × R with a nonzero parallel mean curvature vector (PMC), where R is a Euclidean line. In this paper, we prove a sequence of pinching theorems with respect to the Ricci, sectional and scalar curvatures of M n , which allow us to generalize some classical curvature pinching results in spheres.

Keywords: sectional curvature; Ricci curvature; parallel mean curvature vector; pseudo-umbilical; product space; pinching theorems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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