L2-cohomology and complete Hamiltonian manifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:87

Article

Mazzeo, Rafe¹  Pelayo, Alvaro²  Ratiu, Tudor S.³ 

[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[2] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[3] Ecole Polytech Fed Lausanne, Sect Mathemat, CH-1015 Lausanne, Switzerland

关键词: Symplectic structure;    Hamiltonian action;    L-2-cohomology;   

DOI  :  10.1016/j.geomphys.2014.07.012

来源: Elsevier

【 摘 要 】

A classical theorem of Frankel for compact Kahler manifolds states that a Kahler S-1-action is Hamiltonian if and only if it has fixed points. We prove a metatheorem which says that when the Hodge theory holds on non-compact manifolds, Frankel's theorem still holds. Finally, we present several concrete situations in which the assumptions of the metatheorem hold. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free