CLASSIFICATION OF A FAMILY OF HAMILTONIAN-STATIONARY LAGRANGIAN SUBMANIFOLDS IN COMPLEX HYPERBOLIC 3-SPACE

Abstract

A Lagrangian submanifold in a Kaehler manifold is said to be Hamiltonian-stationary (or simply $H$-stationary) if it is a critical point of the area functional restricted to (compactly supported) Hamiltonian variations. In an earlier paper \cite{cg}, $H$-stationary Lagrangian submanifolds of constant curvature in the complex projective 3-space $CP^3$ with positive relative nullity are classified. In this paper we completely classify $H$-stationary Lagrangian submanifolds of constant curvature in the complex hyperbolic 3-space $CH^3$ with positive relative nullity. As an immediate by-product, several explicit new families of $H$-stationary Lagrangian submanifolds in $CH^3$ are obtained.