Hamiltonian Stationary Lagrangian Tori in Kaehler Manifolds

TL;DR

This paper establishes a curvature condition in four-dimensional Kaehler manifolds that ensures the existence of small Hamiltonian stationary Lagrangian tori, advancing understanding of special Lagrangian submanifolds.

Contribution

It provides a new sufficient curvature condition for the existence of Hamiltonian stationary Lagrangian tori in four-dimensional Kaehler manifolds.

Findings

Curvature condition guarantees existence of tori

Construction of small Hamiltonian stationary Lagrangian tori

Advances in understanding special Lagrangian geometry

Abstract

A Hamiltonian stationary Lagrangian submanifold of a Kaehler manifold is a Lagrangian submanifold whose volume is stationary under Hamiltonian variations. We find a sufficient condition on the curvature of a Kaehler manifold of real dimension four that guarantees the existence of a family of small Hamiltonian stationary Lagrangian tori.