GEOMETRY OF SUBMANIFOLD OF

The geometry of Submanifolds is a very important and useful branch in differential geometry , Since it has many important applications in physics and some other branches of sciences .Based on the above perspectives , the present thesis focus on the study of CR-submanifold of an T- manifold, which is considered as modern extensions of Riemannian manifold theory, and also it is very interesting topic for study and research. We studied comprehensively some theories and properties of CR-submanifold of an T- manifold . Furthermore, we studied CR-product, normal CR-submanifold of an T-manifold and the relation between these two topics.Finally, we studied integrability conditions of distributions, sectional curvature, Ricci tensor and scalar curvature . Moreover, we obtained new results related to the mentioned matters.