International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 1, Pages 17-27
On sectional and bisectional curvature of the -umbilical submanifolds
1Facultatea de Matematică, Universitatea Bucuresti, Str. Academiei 14, Bucuresti 70109, Romania
2Dipartimento di Matematica, Universit'a di Parma, Via D'Azeglio 85, Parma 43100, Italy
Received 20 January 2002
Copyright © 2002 S. Ianus and G. B. Rizza. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be an -umbilical submanifold of an almost Hermitian
manifold . Some relations expressing the difference of
bisectional and of sectional curvatures of and of
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 , and some special cases.