English

Circle actions on almost complex manifolds with isolated fixed points

Differential Geometry 2022-01-06 v2 Symplectic Geometry

Abstract

The author proved that if the circle acts symplectically on a compact, connected symplectic manifold MM with three fixed points, then MM is equivariantly symplectomorphic to some standard action on CP2\mathbb{CP}^2. In this paper, we extend the result to a circle action on an almost complex manifold; if the circle acts on a compact, connected almost complex manifold MM with exactly three fixed points, then dimM=4\dim M=4. Moreover, we deal with the cases of one fixed point and two fixed points.

Keywords

Cite

@article{arxiv.1510.00952,
  title  = {Circle actions on almost complex manifolds with isolated fixed points},
  author = {Donghoon Jang},
  journal= {arXiv preprint arXiv:1510.00952},
  year   = {2022}
}
R2 v1 2026-06-22T11:12:22.767Z