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

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.