Abstract
B.-Y. Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. The Lagrangian version of this inequality was proved by the same author.\newline In this article, we obtain a sharp estimate of the Ricci tensor of a slant submanifold $M$ in a complex space form $\widetilde M(4c)$, in terms of the main extrinsic invariant, namely the squared mean curvature. If, in particular, $M$ is a Kaehlerian slant submanifold which satisfies the equality case identically, then it is minimal.
Citation
Koji Matsumoto. Ion Mihai. Yoshihiko Tazawa. "Ricci tensor of slant submanifolds in complex space forms." Kodai Math. J. 26 (1) 85 - 94, March 2003. https://doi.org/10.2996/kmj/1050496650
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