Applications of stable currents and homology groups in CR-warped products of complex space forms

Abstract

In the present, by using the result Lawson-Simons, we adopt a different technique to show that there is no a stable integral q -currents and a non-trivial homology group in a compact oriented CR-warped product submanifold M n in a complex space forms space Q 2m c (4c) by imposing some restrictions on the squared norm of gradient and the Laplacian of warped function. Finally, we show that the same approach can be gotten using Dirichlet energy, positive eigenvalue and Hamiltonian.