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RICCI CURVATURE OF SUBMANIFOLDS OF AN S-SPACE FORM

  • Published : 2009.09.30

Abstract

Involving the Ricci curvature and the squared mean curvature, we obtain a basic inequality for a submanifold of an S-space form tangent to structure vector fields. Equality cases are also discussed. As applications we find corresponding results for almost semi-invariant submanifolds, $\theta$-slant submanifolds, anti-invariant submanifold and invariant submanifolds. A necessary and sufficient condition for a totally umbilical invariant submanifold of an S-space form to be Einstein is obtained. The inequalities for scalar curvature and a Riemannian invariant $\Theta_k$ of different kind of submanifolds of a S-space form $\tilde{M}(c)$ are obtained.

Keywords

S-space form;almost semi-invariant submanifold;$\theta$-slant submanifold;anti-invariant submanifold;Ricci curvature;k-Ricci curvature;scalar curvature;$\Theta$-invaraint

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