Certain submanifolds in a locally conformal Kaehler manifold

Abstract

In this report, we define two morphisms in a CR-submanifold M in a locally conformal Kaehler manifold  M̃ and consider the parallerisms of these morphisms. Then, using these morphisms, we define a (0,2)-tensor field S in M and consider the normality of M. Finally, we define 3-tensors S⁽¹⁾, S⁽²⁾ and S_(a)⁽³⁾  in an anti-holomorphic submanifold in M̃ and cosider the relations of these tensor fields.