On sectional and bisectional curvature of theH-umbilical submanifolds

摘要

LetMbe anH-umbilical submanifold of an almost HermitianmanifoldM˜. Some relations expressing the difference ofbisectional and of sectional curvatures ofM˜and ofMare obtained. The geometric notion of related bases for a pair oforiented planes permits to write the second members in acompletely geometrical form. When the planes are not orthogonal,more simple formulas are obtained. The paper ends with a remark,concerning the vector fieldJH, and some special cases.