English

On Hamiltonian stationary Lagrangian spheres in non-Einstein Kaehler surfaces

Differential Geometry 2012-12-04 v1

Abstract

Hamiltonian stationary Lagrangian spheres in Kaehler-Einstein surfaces are minimal. We prove that in the family of non-Einstein Kaehler surfaces given by the product Σ1×Σ2\Sigma_1\times\Sigma_2 of two complete orientable Riemannian surfaces of different constant Gauss curvatures, there is only a (non minimal) Hamiltonian stationary Lagrangian sphere. This example is defined when the surfaces Σ1\Sigma_1 and Σ2 \Sigma_2 are spheres.

Keywords

Cite

@article{arxiv.0706.4390,
  title  = {On Hamiltonian stationary Lagrangian spheres in non-Einstein Kaehler surfaces},
  author = {Ildefonso Castro and Francisco Torralbo and Francisco Urbano},
  journal= {arXiv preprint arXiv:0706.4390},
  year   = {2012}
}
R2 v1 2026-06-21T08:50:38.070Z