Some Studies On Quasi-effective Bundles On Non-Kahler Manifolds And Transverse Holomorphic Curvature Of Sasakian Manifold

In this paper,we mainly study pseudo-effecive vector bundles and the transverse holomorphic sectional curvature on Sasakian manifolds.In Chapter 2,we study pseudo-effecive vector bundles on some non-Kahler manifolds.We show that pseudo-effecive vector bundles with vanishing first Chern number on the Hermitian manifold(M,ω)are numerically flat,where the(1,1)-form ω satisfies??ωn-1=0,??ωn-2=0.In Chapter 3,we introducte some basic knowledge about Sasakian geometry and extend some theorems in K?hler manifolds to Sasakian manifolds.In Chapter 4,we study the relationship between the transverse holomorphic sectional curvature and the canonical line bundle of Sasakian manifolds.We use the method of transverse Monge-Ampere equation to prove that compact Sasakian manifolds with negative transverse holomorphic sectional curvature must have positive canonical line bundle,and compact Sasakian manifolds with non-positive transverse holomorphic sectional curvature must have numerically effective canonical line bundle,as a application,we get a Miyaoka-Yau type inequality.