zbMATH — the first resource for mathematics

On sectional and bisectional curvature of the \(H\)-umbilical submanifolds. (English) Zbl 1020.53009
Authors’ summary: Let \(M\) be an \(H\)-umbilical submanifold of an almost Hermitian manifold \(\widetilde M\). Some relations expressing the difference of bisectional and of sectional curvatures of \(\widetilde M\) 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.
53B25 Local submanifolds
53B35 Local differential geometry of Hermitian and Kählerian structures
Full Text: DOI EuDML