The Research Of CR-submanifolds On Weak Kaehlerian Manifold

Bejancu A advanced the theory of the CR-submanifold in the 1970s.A lot of scholars researched characteristics and properties of the CR-submanifold in many kinds of combinations of metrics and manifolds all the time.Bejancu A,Ogiue K and Hsu C J focused on properties of the totally geodesic submanifold and the anti-holomophic CR-submaifold in nearly Kaehler manifold and almost Hermite manifold.Blair D.E.analysed the CR-submanifold of Hermite manifold.And Ornea L.contributed to the CR-submanifold of S-manifold..In the past the decade,Yong Wan went deeply into the geometry of leaves and normal CR-submanifold in contact metric manifold and nearly Kaehler manifold.And Yong Wan introduced weak Kaehler manifold by using structures of Kaehler manifold and nearly Kaehler manifold.We mainly study characteristics of weak Kaehler manifold in this paper and the content are as follows:In the first chapter,we make a brief introduction of the background of research of CR-submanifold and development of almost Hermite manifold.In the second chapter,we make arrangements of all of the required preliminaries of research in weak Kaehler manifold.In the third chapter,we give the main result of the paper in the follow four parts of research of weak Kaehler manifold to deliberate the integrability of distribution D,the integrabinity of distribution D?,geometry of leaves of distribution and normal CR-submanifold in weak Kaehler manifold.