AN IMPROVED CHEN-RICCI INEQUALITY FOR KAEHLERIAN SLANT SUBMANIFOLDS IN COMPLEX SPACE FORMS

Abstract

B. Y. Chen proved in [4] an optimal inequality for Lagrangian submanifolds in complex space forms in terms of the Ricci curvature and the squared mean curvature, well-known as the Chen-Ricci inequality. Recently, the Chen-Ricci inequality was improved in [7, 11] for Lagrangian submanifolds in complex space forms. In this article we extend the improved Chen-Ricci inequality to Kaehlerian slant submanifolds in complex space forms. We also investigate the equality case of the inequality.