Geometrical conditions for the existence of a Milnor vector field

TL;DR

This paper establishes new geometric conditions ensuring the existence of Milnor vector fields for certain singularities, aiding in understanding the equivalence of Milnor fibrations in real and complex cases.

Contribution

It introduces novel sufficient conditions for the existence of Milnor vector fields applicable to new classes of singularities.

Findings

Identified geometric conditions guaranteeing Milnor vector fields

Linked Milnor vector fields to the equivalence of Milnor fibrations

Extended understanding of singularity classes with Milnor fibrations

Abstract

We introduce several sufficient conditions to guarantee the existence of the Milnor vector field for new classes of singularities of map germs. This special vector field is related with the equivalence problem of the Milnor fibrations for real and complex singularities, if they exit.