Semi-slant Submanifolds Of Kaehler Product Manifolds

The semi-slant submanifold is a generalization of holomorphicsubmanifold and totally real submanifold. In this paper, we study someF-invariant product semi-slant submainfolds of a Kaehler productmanifold, and classify these submainfolds. Then they are generalized tothe cases of F-invariant product semi-slant submainfolds of a Kaehlerproduct manifold, and we classify these submainfolds. Some specialcases are studied as well.This paper is divided into three sections. In section one, thehistorical background of the relevant problems is presented and the mainresults are introduced. Section two is preliminaries, in this section weintroduce some basic definitions and properties related to thesedefinitions. Section three is main results and proving processes of theseresults. First of all, Theorem 1 is obtained by the study of a kind ofproduct semi-slant submainfolds of a Kaehler manifold. After gettingLemma, Theorem 2 is obtained by the study of F-invariant semi-slantsubmainfolds of a Kaehler product manifold. After generalized Theorem2 to F -invariant semi-slant submainfolds of a Kaehler product manifold,we get Theorem 3.