Recently, 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. Afterwards, we
dealt with similar problems for submanifolds in
complex space forms. In the present paper, we
obtain sharp inequalities between the Ricci
curvature and the squared mean curvature for
submanifolds in Sasakian space forms. Also,
estimates of the scalar curvature and the
kRicci curvature respectively, in terms of the
squared mean curvature, are proved.
