International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 27, Pages 1731-1738
doi:10.1155/S016117120311215X
B.-Y. Chen inequalities for semislant submanifolds in Sasakian
space forms
Department of Mathematics I, University of Politehnica of Bucharest, Splaiul Independenţei 313, Bucharest 77206, Romania
Received 20 December 2001
Copyright © 2003 Dragoş Cioroboiu. 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
Chen (1993) established a sharp inequality for the sectional
curvature of a submanifold in Riemannian space forms in terms of
the scalar curvature and squared mean curvature. The notion of a
semislant submanifold of a Sasakian manifold was introduced by J.
L. Cabrerizo, A. Carriazo, L. M. Fernandez, and M. Fernandez
(1999). In the present paper, we establish Chen inequalities for
semislant submanifolds in Sasakian space forms by using subspaces
orthogonal to the Reeb vector field ξ.