CONTACT黎曼流形上S.TANNO联络的数量曲率

THE SCAIAR CURVATURE OF S. TANNO'''' CONNECTION ON CONTACT RIEMANNIAN MANIFOLDS

Since S.S.chern and R.S.Hamilton have done the research about a critical metric of the Dirichlet energy Concerning the Webster torsion tensor on three-dimensional Contact manifolds. A lot of new geometric results have been given on Contact ma- nifolds. The Canonical affine Connection on a nondegenrate integr- able CR-manifold Was generalized to the Contact Riemannian manifolds by S.TANND,that richen the geometric Content of Contact manifolds One of the important problems in the study of Contact man- ifolds is to find differential geometric propertieswhich are ind- ependent of the choice of Contact forms. The purpose of this paper is,based on S.TANNO' Connect- ion on Contact Riemannian manifolds,to prove four equivatent Condition Concerning the sectional curvature,and give the for- mulas of the Curvature tensor and sclalar curvature.