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International Journal of Mathematics and Mathematical Sciences
Volume 29, Issue 12, Pages 719-726
http://dx.doi.org/10.1155/S0161171202012863

Ricci curvature of submanifolds in Kenmotsu space forms

1Department of Mathematics, Faculty of Arts and Sciences, Uludag University, Görükle 16059, Bursa, Turkey
2Faculty of Mathematics, University of Bucharest, Str. Academiei 14, Bucharest 70109, Romania

Received 20 April 2001; Revised 21 August 2001

Copyright © 2002 Hindawi Publishing Corporation. 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

In 1999, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Similar problems for submanifolds in complex space forms were studied by Matsumoto et al. In this paper, we obtain sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in Kenmotsu space forms.