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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Wang-Hua Qiu & Xin Zhan, 2023. "Curvature Pinching Problems for Compact Pseudo-Umbilical PMC Submanifolds in S m ( c ) × R," Mathematics, MDPI, vol. 12(1), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:68-:d:1306991
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