On Ricci curvature ofC-totally real submanifolds in Sasakian space forms期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Liu Ximin

Affiliation:	(1) Department of Applied Mathematics, Dalian University of Technology, 116 024 Dalian, China;(2) Present address: Department of Mathematical Sciences, Rutgers University, 08102 Camden, New Jersey, USA

Abstract:	LetM ⁿ be a Riemanniann-manifold. Denote byS(p) and Ric(p) the Ricci tensor and the maximum Ricci curvature onM _n, respectively. In this paper we prove that everyC-totally real submanifold of a Sasakian space formM ^2m+1(c) satisfies $S leqslant (frac{{(n - 1)(c + 3)}}{4}) + frac{{n^2 }}{4}H^2 )g$ , whereH ² andg are the square mean curvature function and metric tensor onM ⁿ, respectively. The equality holds identically if and only if eitherM ⁿ is totally geodesic submanifold or n = 2 andM ⁿ is totally umbilical submanifold. Also we show that if aC-totally real submanifoldM ⁿ ofM ²ⁿ⁺¹ (c) satisfies $overline {Ric} = frac{{(n - 1)(c + 3)}}{4} + frac{{n^2 }}{4}H^2$ identically, then it is minimal.

Keywords:	Ricci curvature C-totally real submanifold Sasakian space form
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