Certain circle actions on Kaehler manifolds

Abstract

Let the circle act holomorphically on a compact Kähler manifold $M$ of complex dimension $n$ with moment map $\varphi :M\to \mathbb{R}$. Assume the critical set of $\varphi$ consists of 3 connected components, the extrema being isolated points. We show that $M$ is equivariantly biholomorphic to $\CP^n$, where $n\ge 2$, or to $\Tilde G_2(\R^{n+2})$, the Grassmannian of oriented 2-planes in ${\mathbb{R}}^{n+2}$, where $n\ge 3$, with a standard circle action; we also show that $M$ is equivariantly symplectomorphic to $\CP^n$, where $n\ge 2$, or to $\Tilde G_2(\R^{n+2})$, where $n\ge 3$, with a standard circle action.

References in corpus (2)

• Some 6-dimensional Hamiltonian S^1 manifolds
• Hamiltonian circle actions with minimal fixed sets

Cited by in corpus (4)

• Hamiltonian circle actions on eight dimensional manifolds with minimal fixed sets
• One-connectivity and finiteness of Hamiltonian $S^1$-manifolds with minimal fixed sets
• Hamiltonian circle actions with minimal isolated fixed points
• Hamiltonian circle actions with fixed point set almost minimal