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