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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 231416, 11 pages
http://dx.doi.org/10.1155/2012/231416
Research Article

A Basic Inequality for the Tanaka-Webster Connection

1Department of Mathematics, Dongguk University, Gyeongju 780-714, Republic of Korea
2Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea

Received 7 November 2011; Accepted 28 November 2011

Academic Editor: C. Conca

Copyright © 2012 Dae Ho Jin and Jae Won Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For submanifolds tangent to the structure vector field in Sasakian space forms, we establish a Chen's basic inequality between the main intrinsic invariants of the submanifold (namely, its pseudosectional curvature and pseudosectional curvature on one side) and the main extrinsic invariant (namely, squared pseudomean curvature on the other side) with respect to the Tanaka-Webster connection. Moreover, involving the pseudo-Ricci curvature and the squared pseudo-mean curvature, we obtain a basic inequality for submanifolds of a Sasakian space form tangent to the structure vector field in terms of the Tanaka-Webster connection.