On contact metric manifold with ξN(k)

Abstract

The object of the present paper is to study contact metric manifold with (kN . An irrotational pseudo projective curvature tensor in a contact metric manifold with ) (kN is considered. Here it is proved that under this consideration an n-dimensional contact metric manifold with) (kN is either locally isometric to the Riemannian product )4( )0(1 n n S E   or is a space of constant curvature k. Finally, we study conharmonically flat contact metric manifold with ) (kN satisfying R(X,Y).S=0 and here it is proved that the symmetric endomorphism Q of tangent space corresponding to S has two different nonzero eigen values (n − 1)k and −2(n − 1)k.