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International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 1, Pages 17-27
http://dx.doi.org/10.1155/S0161171202201167

On sectional and bisectional curvature of the H-umbilical submanifolds

1Facultatea de Matematică, Universitatea Bucuresti, Str. Academiei 14, Bucuresti 70109, Romania
2Dipartimento di Matematica, Universit'a di Parma, Via D'Azeglio 85, Parma 43100, Italy

Received 20 January 2002

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let M be an H-umbilical submanifold of an almost Hermitian manifold M˜. Some relations expressing the difference of bisectional and of sectional curvatures of M˜ and of M are obtained. The geometric notion of related bases for a pair of oriented planes permits to write the second members in a completely geometrical form. When the planes are not orthogonal, more simple formulas are obtained. The paper ends with a remark, concerning the vector field JH, and some special cases.