RICCI CURVATURE OF INTEGRAL SUBMANIFOLDS OF AN S-SPACE FORM

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 44, Issue 3, 2007, pp.395-406
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2007.44.3.395

Title & Authors

RICCI CURVATURE OF INTEGRAL 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 an integral submanifold of an S-space form. By polarization, we get a basic inequality for Ricci tensor also. Equality cases are also discussed. By giving a very simple proof we show that if an integral submanifold of maximum dimension of an S-space form satisfies the equality case, then it must be minimal. These results are applied to get corresponding results for C-totally real submanifolds of a Sasakian space form and for totally real submanifolds of a complex space form.

Keywords

S-space form;integral submanifold;C-totally real submanifold;totally real submanifold;Lagrangian submanifold;Ricci curvature;k-Ricci curvature;scalar curvature;

Language

English

Cited by

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