Localization Formulas About Two Killing Vector Fields

TL;DR

This paper develops localization formulas for characteristic numbers on manifolds with two Killing vector fields, using invariant forms and extending classical localization techniques.

Contribution

It introduces new localization formulas involving two Killing vector fields, expanding the scope of classical localization methods in differential geometry.

Findings

Derived localization formulas for characteristic numbers.

Extended classical localization techniques to cases with two Killing vector fields.

Provided applications to characteristic number computations.

Abstract

In this article, we will discuss the smooth $(X_{M}+\sqrt{-1}Y_{M})$-invariant forms on $M$ and to establish a localization formulas. As an application, we get a localization formulas for characteristic numbers.