Two Classes Of Semi-Symmetric Non-metric Connections On Kenmotsu Manifold

This thesis mainly study some properties of two classes of semi-symmetric non-metric connections on Kenmotsu manifold.We give the curvature operator and curvature tensor and the first Bianchi identity of the Kenmotsu manifold with respect to the first class of semi-symmetric non-metric connection (?),and get the condition that Kenmotsu manifold is an ?Einstein manifold about the first class of semi-symmetric non-metric connection(?).Furthermore some relations of the curvature tensor on Kenmotsu manifold are obtained when the Kenmotsu manifold is a locally flat manifold with respect to (?).Combining with the characteristics of Kenmotsu manifold,we give the cur-vature tensor,Ricci curvature,scalar curvature,conformal curvature,conharmonic curvature and projective curvature tensor of the Kenmotsu manifold with respect to the second class of semi-symmetric non-metric connection (?),and define the ?conharmonically flat,projectively flat,? projectively flat,semi-symmetric,locally symmetric and covariant constant of the Kenmotsu manifold with respect to the second class of semi-symmetric non-metric connection (?),and give the def-inition that the manifold is recurrent with respect to the Levi-Civita connection.Some relations of the conformal curvature,conharmonic curvature and projective curvature tensor on Kenmotsu manifold are obtained with respect to the second class of semi-symmetric non-metric connection (?) and Riemannian connection (?).The research get the condition that Kenmotsu manifold is an ? Einstein manifold about the second class of semi-symmetric non-metric connection ? and Riemannian connection ?,the corresponding proof is given.This thesis is divided into 4 chapters.In the first two chapters of this pa-per,we introduce the research status of semi-symmetric non-metric connection,the basic knowledge of Riemann manifolds,Kenmotsu manifold and two classes of semi-symmetric non-metric connections (?).Then we get the curvature of the Kenmotsu manifold with respect to (?) in the third chapter.In the chapter four,we discuss the flatness of the Kenmotsu manifold about two classes of semi-symmetric non-metric connections (?).