Circle actions on almost complex manifolds with isolated fixed points

Abstract

The author proved that if the circle acts symplectically on a compact, connected symplectic manifold $M$ with three fixed points, then $M$ is equivariantly symplectomorphic to some standard action on $\mathbb{CP}^2$. 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 $M$ with exactly three fixed points, then $\dim M=4$. Moreover, we deal with the cases of one fixed point and two fixed points.