Common Singularities of Commuting Vector Fields

TL;DR

This paper investigates the nature of singular points in pairs of commuting vector fields on real submanifolds within Kähler manifolds, aiming to classify and understand their common singularities.

Contribution

It provides a new analysis of the structure and classification of singularities arising from commuting vector fields in the context of Kähler geometry.

Findings

Identification of conditions for common singularities

Classification results for singularities of commuting vector fields

Insights into the geometric structure of these singularities

Abstract

We study the singularities of commuting vector fields of a real submanifold of a K\"ahler manifold $Z$.