International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 11, Pages 711-716
doi:10.1155/S0161171203201137

A note on Chen's basic equality for submanifolds in a Sasakian space form

Mukut Mani Tripathi,1 Jeong-Sik Kim,2 and Seon-Bu Kim3

1Department of Mathematics and Astronomy, Lucknow University, Lucknow 226 007, India
2Department of Mathematics Education, Sunchon National University, Sunchon 540-742, Korea
3Department of Mathematics, Chonnam National University, Kwangju 500-757, Korea

Received 28 January 2002

Copyright © 2003 Mukut Mani Tripathi et al. 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

It is proved that a Riemannian manifold M isometrically immersed in a Sasakian space form M˜(c) of constant φ-sectional curvature c<1, with the structure vector field ξ tangent to M, satisfies Chen's basic equality if and only if it is a 3-dimensional minimal invariant submanifold.