Local Dynamics of Conformal Vector Fields

TL;DR

This paper investigates the local behavior of conformal vector fields near singularities across various pseudo-Riemannian types, providing a comprehensive analysis in the Riemannian case using geometric and dynamical methods.

Contribution

It offers a complete classification of local forms of conformal vector fields near singularities in Riemannian geometry, extending understanding to general pseudo-Riemannian contexts.

Findings

Complete local classification in Riemannian case

Analysis of local dynamics of conformal transformations

Extension to general pseudo-Riemannian types

Abstract

The aim of the paper is to understand the local forms of conformal vector fields in the neighborhood of a singularity. We begin a general study in this direction, for any pseudo-Riemannian type, and give a complete answer in the Riemannian case. This is done using geometric methods, and studying local dynamics of sequences of conformal transformations.