Kragujevac J. Math. 26 (2004) 83-88.

Abstract. For a totally real surface M of a complex space form M(4c) of arbitrary codimension, we obtain an inequality relating the squared mean curvature ||H|| ², the holomorphic sectional curvature c, the Gauss curvature K and the elliptic curvature K^E of the surface. Using the notion of ellipse of curvature, we obtain a characterization of the equality. An example of a Lagrangian surface of C² satisfying the equality case is given.