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Ricci curvature of integral submanifolds of an $\mathcal{S}$-space form

Mukut Mani Tripathi|김정식|Mohit Kumar Dwivedi
대한수학회 (The Korean Mathematical Society)|2007.08|대한수학회보 (Bulletin of the KMS)|제44권 제3호|pp. 395-406

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Abstract

Involving the Ricci curvature and the squared mean curva-ture, we obtain a basic inequality for an integral submanifold of an S-space form. By polarization, we get a basic inequality for Ricci tensoralso. Equality cases are also discussed. By giving a very simple proof weshow that if an integral submanifold of maximum dimension of an S-spaceform satises the equality case, then it must be minimal. These resultsare applied to get corresponding results forC-totally real submanifoldsof a Sasakian space form and for totally real submanifolds of a complexspace form.

참고문헌 (14)

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