Abstract
Our main objective of this paper is to derive the relationship between the main extrinsic invariant, and the contact CR δ-invariant (new intrinsic invariant) on a generic submanifold in trans-Sasakian generalized Sasakian space forms. Further, we find a lower bound of the squared norm of the mean curvature (main extrinsic invariant) in terms of a CR δ-intrinsic invariant, and the Laplacian of the warping function for CR-warped products in the same ambient space forms. We also investigate the classifications and triviality of connected, compact CR-warped product manifolds isometrically immersed into the trans-Sasakian generalized Sasakian space forms.