Mathematische Zeitschrift

, Volume 271, Issue 1–2, pp 257–270 | Cite as

On Hamiltonian stationary Lagrangian spheres in non-Einstein Kähler surfaces

  • Ildefonso Castro
  • Francisco Torralbo
  • Francisco Urbano


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


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Ildefonso Castro
    • 1
  • Francisco Torralbo
    • 2
  • Francisco Urbano
    • 2
  1. 1.Departamento de MatemáticasUniversidad de JaénJaénSpain
  2. 2.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaSpain

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