Kaehler Submanifolds And Totally Real Submanifolds In A Locally Symmetric Bochner-Kaehler Manifold

In this thesis,we study several problems of Kaehler submanifolds and totally real submanifolds in a locally symmetric Bochner-Kaehler manifold.The main results of the thesis are as follows:Theorem 1 M^n+Pis a locally symmetric Bochner-Kaehler manifold,Let Mⁿ be a compact Kaehler submanifold with flat normal bundle in M^n+P.If the infimum of sectional curvature R_c in Mⁿ satisfies: then Mⁿ must be totally geodesic in M^n+P,(T_c is the supremum of Ricci curvature and t_c is the infimum of Ricci curvature in M^n+P).Theorem 2 Let Mⁿ be a compact totally real minimal submanifold in Mⁿ which is a locally symmetric Bochner-Kaehler manifold.If the infimum of sectional curvature R_c in Mⁿ satisfies: then Mⁿ must be totally geodesic in Mⁿ.Theorem 3 Let Mⁿ be a compact totally real 2-harmonic submanifold in Mⁿ which is a locally symmetric Bochner-Kaehler manifold.If Ricci curvature of Mⁿ is nonegative and positive at a point at least,then the holomorphic sectional curvature of Mⁿ is a postive constant number.Theorem 4 There is no compact totally real 2-harmonic submanifold with non-zero parallel mean curvature and positive sectional curvature in a locally symmetric Bochner -Kaehler manifold.