The Studies Of Some Submanifolds In Generalized Complex Space Forms

In this paper,we study the relationships between the intrinsic invariants and the extrinsic invariants of bi-slant submanifolds,semi-slant submanifolds, semi-invariant sub-manifolds and slant submanifolds in generalized complex space forms . We obtain two inequalities ,one is about Ricci curvature and mean curvature,the other is about mean curvature and a Riemannian invariant.The conditions are also studied under which the left and right parts of the inequalities are equal.Four sections are included in the paper . Section one devote to some preliminaries..We study the bi-slant submanifolds,semi-slant submanifolds, semi-invariant submanifolds and slant submanifolds in section two.The definition of generalized complex space forms is included in section three.Section four is mainly about the submanifolds in generalized complex space forms.First we study curvature operator and Ricci curvature tensor of the submanifolds in it .Then an inequality about Ricci curvature and mean curvature is given ,so is the conditions of equality .Finally we obtain an inequality about mean curvature and a Riemannian invariant in this section .