Ricci Soliton of CR-Warped Product Manifolds and Their Classifications

In this article, we derived an equality for CR-warped product in a complex space form which forms the relationship between the gradient and Laplacian of the warping function and second fundamental form. We derived the necessary conditions of a CR-warped product submanifolds in Ka center dot hler manifold to be an Einstein manifold in the impact of gradient Ricci soliton. Some classification of CR-warped product submanifolds in the Ka center dot hler manifold by using the Euler-Lagrange equation, Dirichlet energy and Hamiltonian is given. We also derive some characterizations of Einstein warped product manifolds under the impact of Ricci Curvature and Divergence of Hessian tensor.