SOME INEQUALITIES OF ANTI-INVARIANT RIEMANNIAN SUBMERSIONS IN COMPLEX SPACE FORMS

B.-Y. Chen revealed the intrinsic and extrinsic invariants who established an inequality including Ricci curvature and squared mean curvature of a submanifold in a real space form Rn(c) in 1999 (see [4]). In 2005 by B.-Y. Chen, a generalization of this inequality was proved for arbitrary submanifolds in an arbitrary Riemannian manifold (see [5]). Subsequently, this inequality has been comprehensively examined for different ambient spaces by some authors who are achieved some results (see [3,7, 16, 19, 22, 25]). A C infinity-submersion phi can be defined according to the following conditions: a (pseudo)-Riemannian submersion [1, 8,12,17, 20, 21], an almost Hermitian submersion [23], a quaternionic submersion [13] , a slant submersion [11], a Clairaut Submerpecially, by utilizing the notion of almost Hermitian submersions, B. Watson [23]