# 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.
##### MSC:
 53B25 Local submanifolds 53B35 Local differential geometry of Hermitian and Kählerian structures
Full Text: