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http://dx.doi.org/10.4134/BKMS.2009.46.5.979

RICCI CURVATURE OF SUBMANIFOLDS OF AN S-SPACE FORM  

Kim, Jeong-Sik (DEPARTMENT OF MATHEMATICS AND MATHEMATICAL INFORMATION YOSU NATIONAL UNIVERSITY)
Dwivedi, Mohit Kumar (DEPARTMENT OF MATHEMATICS AND ASTRONOMY LUCKNOW UNIVERSITY)
Tripathi, Mukut Mani (DEPARTMENT OF MATHEMATICS BANARAS HINDU UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.46, no.5, 2009 , pp. 979-998 More about this Journal
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;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
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