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On sectional and bisectional curvature of the H -umbilical submanifolds

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  • S. Ianus
  • G. B. Rizza

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.

Suggested Citation

  • S. Ianus & G. B. Rizza, 2002. "On sectional and bisectional curvature of the H -umbilical submanifolds," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 32, pages 1-11, January.
    • Handle: RePEc:hin:jijmms:584109
    DOI: 10.1155/S0161171202201167
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