• On Ricci curvature ofC-totally real submanifolds in Sasakian space forms

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      https://www.ias.ac.in/article/fulltext/pmsc/111/04/0399-0405

    • Keywords

       

      Ricci curvature; C-totally real submanifold; Sasakian space form

    • Abstract

       

      LetMn be a Riemanniann-manifold. Denote byS(p) and Ric(p) the Ricci tensor and the maximum Ricci curvature onMn, respectively. In this paper we prove that everyC-totally real submanifold of a Sasakian space formM2m+1(c) satisfies$$S \leqslant (\frac{{(n - 1)(c + 3)}}{4}) + \frac{{n^2 }}{4}H^2 )g$$, whereH2 andg are the square mean curvature function and metric tensor onMn, respectively. The equality holds identically if and only if eitherMn is totally geodesic submanifold or n = 2 andMn is totally umbilical submanifold. Also we show that if aC-totally real submanifoldMn ofM2n+1 (c) satisfies$$\overline {Ric} = \frac{{(n - 1)(c + 3)}}{4} + \frac{{n^2 }}{4}H^2 $$ identically, then it is minimal.

    • Author Affiliations

       

      Liu Ximin1 2

      1. Department of Applied Mathematics, Dalian University of Technology, Dalian - 116 024, China
      2. Department of Mathematical Sciences, Rutgers University, Camden, New Jersey - 08102, USA
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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