RICCI CURVATURE OF SUBMANIFOLDS OF AN S-SPACE FORM

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 46, Issue 5, 2009, pp.979-998
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2009.46.5.979

Title & Authors

RICCI CURVATURE OF SUBMANIFOLDS OF AN S-SPACE FORM

Kim, Jeong-Sik; Dwivedi, Mohit Kumar; Tripathi, Mukut Mani;

Kim, Jeong-Sik; Dwivedi, Mohit Kumar; Tripathi, Mukut Mani;

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, -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 of different kind of submanifolds of a S-space form are obtained.

Keywords

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

Language

English

Cited by

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