Ricci curvature for submanifolds of Bochner Kahler manifold

TL;DR

This paper extends the known relationship between Ricci curvature and mean curvature from Riemannian space forms to submanifolds within Bochner Kahler manifolds, broadening the understanding of curvature interactions in complex geometry.

Contribution

It generalizes the Ricci and mean curvature relationship to submanifolds of Bochner Kahler manifolds, a new setting in differential geometry.

Findings

Established a generalized curvature relationship for submanifolds in Bochner Kahler manifolds.

Extended classical results from Riemannian space forms to complex geometry contexts.

Abstract

B. Y. Chen establish the relationship between the Ricci curvature and the squared mean curvature for submanifolds of Riemannian space form with arbitrary codimension. In this paper, we generalize the relationship between the Ricci curvature and the squared norm of mean curvature vector for submanifolds of Bochner Kahler manifolds.