Kodai Mathematical Journal
Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991
Ricci tensor of slant submanifolds in complex space forms
Koji MatsumotoIon MihaiYoshihiko Tazawa
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2003 Volume 26 Issue 1 Pages 85-94

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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.
In this article, we obtain a sharp estimate of the Ricci tensor of a slant submanifold M in a complex space form ˜{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.
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© Department of Mathematics, Tokyo Institute of Technology
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