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We improve Chen-Ricci inequalities for a Lagrangian submanifold M n of dimension n (n 2) in a 2n -dimensional complex space form M 2n (4c) of constant holomorphic sectional curvature 4c with a semi-symmetric metric connection and a Legendrian submanifold M n in a Sasakian space form M 2n+1 (c) of constant ϕ -sectional curvature c with a semi-symmetric metric connection, respectively. Mathematics subject classification (2010): 53C40, 53B05, 53B15.doi:10.7153/jmi-09-67 fatcat:l6lwyy7wcnbvni2fx6bnzrrozm