Lagrangian surfaces with circullar ellipse of curvature in complex space forms

Abstract

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 of the complex projective plane and of the Whitney spheres in the complex projective, complex Euclidean and complex hyperbolic planes.

9 pages. To appear in Mathematical Proceedings of the Cambridge Philosophical Society