On Hamiltonian stationary Lagrangian spheres in non-Einstein Kaehler surfaces

Details On Hamiltonian stationary Lagrangian spheres in non-Einstein Kaehler surfaces On Hamiltonian stationary Lagrangian spheres in non-Einstein Kaehler surfaces

2007-06-29

arxiv.org/abs/0706.4390v1

Mathematics

Differential Geometry

14 pages, 1 figure

Scientific paper

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 $\Sigma_1\times\Sigma_2$ 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 $\Sigma_1$ and $ \Sigma_2$ are spheres.

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