We investigate the topology of complete Riemannian manifolds with the radial curvature at the base manifold bounded below by those of model surfaces. Here, model surfaces are generalized surfaces of revolution and warped product models which are diffeomorphic to S.

The purpose of this paper is to provide the complete classifications second fundamental form inequality for a warped product pointwise semi-slant submanifold in Kaehler manifold which was obtained by Şahin [Th. 5.2, Warped manifold, Port. Math. 2013] terms intrinsic and extrinsic invariants. In paper, we give some conditions that are not addressed or considered cited mentioned above. Finally, n...

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