On Legendre Submanifolds in Lorentzian Sasakian Space Forms

In this paper, we determine the sectional curvature K(X, Y) of a Legendre submanifold M-n in Lorentzian Sasakian space forms (M-1) over bar (2n+1)(k). Thus, we find the Ricci tensor rho and the scalar curvature tau of Legendre submanifold M-n. From these, we get the equivalent condition with M-n totally geodesic. Next, we prove that Legendre surfaces M-2 in Lorentzian Sasakian space forms (M-1) over bar (5)(k) with C-parallel mean 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).