RICCI CURVATURE OF INTEGRAL SUBMANIFOLDS OF AN S-SPACE FORM

Title & Authors
RICCI CURVATURE OF INTEGRAL SUBMANIFOLDS OF AN S-SPACE FORM
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
1.
RICCI CURVATURE OF SUBMANIFOLDS OF AN S-SPACE FORM,;;;

대한수학회보, 2009. vol.46. 5, pp.979-998
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Chen-Tripathi Inequality for Warped Product Submanifolds of S-space Forms, Annals of the Alexandru Ioan Cuza University - Mathematics, 2012, 58, 1
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Improved Chen–Ricci inequality for curvature-like tensors and its applications, Differential Geometry and its Applications, 2011, 29, 5, 685
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RICCI CURVATURE OF SUBMANIFOLDS OF AN S-SPACE FORM, Bulletin of the Korean Mathematical Society, 2009, 46, 5, 979
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