C-totally real submanifolds in (κ,μ)-contact space forms

We obtain a basic B.-Y. Chen's inequality for a C-totally real submanifold in a (kappa, mu)-contact space form involving intrinsic invariants, namely the scalar curvature and the sectional curvatures of the submanifold on left hand side and the main extrinsic invariant, namely the squared mean curvature on the right hand side. Inequalities between the squared mean curvature and Ricci curvature and between the squared mean curvature and kappa-Ricci curvature are also obtained. These results axe applied to get corresponding results for C-totally real submanifolds in a Sasakian space form.