Abstract
In the present paper, we prove that if Laplacian for the warping function of complete warped product submanifold M-m = B-p x(h) F-q in a unit sphere Sm+k satisfies some extrinsic inequalities depending on the dimensions of the base B-p and fiber F-q such that the base B-p is minimal, then M-m must be diffeomorphic to a unit sphere S-m. Moreover, we give some geometrical classification in terms of Euler-Lagrange equation and Hamiltonian of the warped function. We also discuss some related results.