  We obtain a basic inequality involving the Laplacian of the warping function
and the squared mean curvature of any warped product isometrically immersed in
a Riemannian manifold without assuming any restriction on the Riemann curvature
tensor of the ambient manifold. Applying this general theory, we obtain basic
inequalities involving the Laplacian of the warping function and the squared
mean curvature of $C$-totally real warped product submanifolds of $(\kappa ,\mu
) $-space forms, Sasakian space forms and non-Sasakian $(\kappa ,\mu)
$-manifolds. Then we obtain obstructions to the existence of minimal isometric
immersions of $C$-totally real warped product submanifolds in $(\kappa ,\mu)
$-space forms, non-Sasakian $(\kappa ,\mu) $-manifolds and Sasakian space
forms. In the last, we obtain an example of a warped product $C$-totally real
submanifold of a non-Sasakian $(\kappa ,\mu) $-manifold, which satisfies the
equality case of the basic inequality.
