Translating Solitons in a Lorentzian Setting, Submersions and Cohomogeneity One Actions

TL;DR

This paper introduces new classes of translating solitons in Minkowski space, utilizing submersions and symmetry actions, and provides a complete classification of certain invariant solutions.

Contribution

It develops a general framework for constructing translating solitons using submersions and symmetry, extending classical Euclidean examples to Lorentzian geometry.

Findings

Classified all timelike, invariant translating solitons by rotations and boosts in Minkowski space.

Established a unified approach for translating solitons in Lorentzian and Euclidean settings.

Provided explicit examples of translating solitons in Minkowski space.

Abstract

We study new examples of translating solitons of the mean curvature flow, especially in Minkowski space. We consider for this purpose manifolds admitting submersions and cohomegeneity one actions by isometries on suitable open subsets. This general setting also covers the classical Euclidean examples. As an application, we completely classify timelike, invariant translating solitons by rotations and boosts in Minkowski space.