The Existence of Hamiltonian Stationary Lagrangian Tori in K?hler Manifolds of Any Dimension
Journal
arXiv: 1001.3861
Pages
-
Date Issued
2010
Date
2010
Author(s)
Abstract
Hamiltonian stationary Lagrangians are Lagrangian submanifolds that are critical points of the volume functional under Hamiltonian deformations. They are natural generalizations of special Lagrangians or Lagrangian and minimal submanifolds. In this paper, we obtain a local condition that gives the existence of a smooth family of Hamiltonian stationary Lagrangian tori in Kähler manifolds. This criterion involves a weighted sum of holomorphic sectional curvatures. It can be considered as a complex analogue of the scalar curvature when the weighting are the same. The problem is also studied by Butscher and Corvino (Hamiltonian stationary tori in Kahler manifolds, 2008). © 2011 Springer-Verlag.
Type
journal article
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