Classification of Lagrangian surfaces of constant curvature in complex hyperbolic plane

Abstract

From Riemannian geometric point of view, one of the most fundamental problems in the study of Lagrangian submanifolds is the classification of Lagrangian immersions of real space forms in complex space forms. In earlier papers [B.Y. Chen, Maslovian Lagrangian surfaces of constant curvature in complex projective or complex hyperbolic planes, Math. Nachr.; B.Y. Chen, Classification of Lagrangian surfaces of constant curvature in complex projective planes, J. Geom. Phys. 55 (2005) 399–439], the author classified Lagrangian surfaces of constant curvature in complex projective plane and in complex Euclidean plane. The purpose of this article is thus to provide sixty-one families of Lagrangian surfaces of constant curvature in C H 2 towards the complete classification of Lagrangian surfaces of constant curvature in C H 2 . As an immediate by-product, many new examples of Lagrangian surfaces of constant curvature in C H 2 are discovered.