On Legendre Submanifolds in Lorentzian Sasakian Space Forms

In this paper,we determine the sectional curvature K(X, Y ) of aLegendre submanifold Mn in Lorentzian Sasakian space forms M1 2n+1 (k). Thus, we find the Ricci tensor ρ and the scalar curvature τ of Legendre submanifold Mn. From these, we get the equivalent condition with Mn totally geodesic. Next, we prove that Legendre surfaces M2 in Lorentzian Sasakian space forms M1 5 (k) with C-parallelmean curvature vector field are minimal or locally product of two curves. Moreover, we study Legendre surfaces whose mean curvature vector fields are eigenvectors of the Laplace operator (in normal bundle).