Abstract We consider real hypersurfaces M in complex projective space equipped with both the Levi–Civita and generalized Tanaka–Webster connections. For any nonnull constant k symmetric tensor field of type (1, 1) L on , we can define two fields 2) $$L_F^{(k)}$$ L F (</mm...

We classify the Lagrangian orientable surfaces in complex space forms with the property that the ellipse of curvature is always a circle. As a consequence, we obtain new characterizations of the Clifford torus in the complex projective plane and of the Whitney spheres in the complex projective, complex Euclidean and complex hyperbolic planes. MSC 2000: 53C42, 53C40.