  In this paper, we obtain a basic Chen's inequality for a C-totally real
submanifold in a generalized $(\kappa ,\mu)$-contact space forms 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 $k$-Ricci curvature are also obtained.
