Hamiltonian Stationary Lagrangian Surfaces with Non-Negative Gaussian Curvature in Kähler-Einstein Surfaces

2024/01/19 by Coulibaly, Patrik
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.10517

Abstract

In this paper, we give some simple conditions under which a Hamiltonian stationary Lagrangian submanifold of a Kähler-Einstein manifold must have a Euclidean factor or be a fiber bundle over a circle. We also characterize the Hamiltonian stationary Lagrangian surfaces whose Gaussian curvature is non-negative and whose mean curvature vector is in some L^p space when the ambient space is a simply connected complex space form.

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