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C-totally real submanifolds in (κ,μ)-contact space forms

Published online by Cambridge University Press:  17 April 2009

Mukut Mani Tripathi  and
Jeong-Sik Kim
Mukut Mani Tripathi
Affiliation:
Department of Mathematics and Astronomy, Lucknow University, Lucknow 226 007, India, e-mail: mm-tripathi@hotmail.com
Jeong-Sik Kim
Affiliation:
Department of Mathematics education, Sunchon National University, Sunchon 540-742, Korea, e-mail: jskim01@hanmir.com
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Abstract

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We obtain a basic B,-Y. Chen's inequality for a C-totally real submanifold in a (κ,μ)-contact space form involving intrinsic invariants, namely the scalar curvature and the sectional curvatures of the submanifold on left hand side and the main extrinsic invariant, namely the squared mean curvature on the right hand side. Inequalities between the squared mean curvature and Ricci curvature and between the squared mean curvature and κ-Ricci curvature are also obtained. These results are applied to get corresponding results for C-totally real submanifolds in a Sasakian space form.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 51 - 65
Copyright
Copyright © Australian Mathematical Society 2003

References

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