On Ricci Curvature of C-totally Real Submanifolds in Sasakian Space Forms
نویسنده
چکیده
Let Mn be a Riemannian n-manifold. Denote by S(p) and Ric(p) the Ricci tensor and the maximum Ricci curvature on Mn, respectively. In this paper we prove that every C-totally real submanifolds of a Sasakian space form M̄2m+1(c) satisfies S ≤ ( (n−1)(c+3) 4 + n 2 4 H2)g, where H2 and g are the square mean curvature function and metric tensor on Mn, respectively. The equality holds identically if and only if either Mn is totally geodesic submanifold or n = 2 and Mn is totally umbilical submanifold. Also we show that if a Ctotally real submanifold Mn of M̄2n+1(c) satisfies Ric = (n−1)(c+3) 4 + n 2 4 H2 identically, then it is minimal.
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