A Remark on the Localization formulas about two Killing vector fields

Abstract

In this article, we will discuss a localization formulas of equivariant cohomology about two Killing vector fields on the set of zero points $\mathrm{Zero}(X_M-\sqrt{-1}{Y}_M)=\{x\in M\mid |Y_M(x)|=|X_M(x)|=0\}.$ As application, we use it to get formulas about characteristic numbers and to get a Duistermaat-Heckman type formula on symplectic manifold.

arXiv comment13 pages. arXiv admin note: substantial text overlap with arXiv:1304.3806