Ricci flow of Kaehlerian slant submanifolds in complex space forms and its applications

Abstract

The normalized Ricci flow converges to a constant curvature metric for a connected Kaehlerian slant submanifold in a complex space form if the squared norm of the second fundamental form satisfies certain upper bounds. These bounds include the constant sectional curvature, the slant angle, and the squared norm of the mean curvature vector. Additionally, we demonstrate that the submanifold is diffeomorphic to the sphere \(\mathbb {S}^{n_1}\) under some restriction on the mean curvature. We claim that some of our previous results are rare cases.