Almost all Lagrangian torus orbits in ${\mathbb C}P^n$ are not Hamiltonian volume minimizing

Hiroshi Iriyeh; Hajime Ono

Almost all Lagrangian torus orbits in ${\mathbb C}P^n$ are not Hamiltonian volume minimizing

Differential Geometry 2015-12-08 v1 Symplectic Geometry

Authors: Hiroshi Iriyeh , Hajime Ono

Abstract

All principal orbits of the standard Hamiltonian $T^n$ -action on the complex projective space ${\mathbb C}P^n$ are Lagrangian tori.In this article, we prove that most of them are not volume minimizing under Hamiltonian isotopies of ${\mathbb C}P^n$ if the complex dimension $n$ is greater than two, although they are Hamiltonian minimal and Hamiltonian stable.

Keywords

Lagrangian torus Hamiltonian action complex projective space volume minimization Hamiltonian isotopy Hamiltonian minimal

Cite

@article{arxiv.1512.01940,
  title  = {Almost all Lagrangian torus orbits in ${\mathbb C}P^n$ are not Hamiltonian volume minimizing},
  author = {Hiroshi Iriyeh and Hajime Ono},
  journal= {arXiv preprint arXiv:1512.01940},
  year   = {2015}
}

Comments

14 pages. arXiv admin note: text overlap with arXiv:1408.5576

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