On sectional and bisectional curvature of the H -umbilical submanifolds

S. Ianus and G. B. Rizza

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 32, 1-11

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 J H , and some special cases.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:584109

DOI: 10.1155/S0161171202201167

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