# Extending Translating Solitons in Semi-Riemannian Manifolds

## TL;DR

This paper explores the properties and classifications of translating solitons in semi-Riemannian manifolds, focusing on those invariant under Lie group actions, analyzing their behavior near singularities and at infinity, and providing illustrative examples.

## Contribution

It extends the theory of translating solitons in semi-Riemannian manifolds by examining invariant solutions and their asymptotic behavior, including new examples.

## Key findings

- Characterization of invariant translating solitons
- Analysis of behavior near singular orbits and at infinity
- Construction of new examples of such solitons

## Abstract

In this paper, we recall some general properties and theorems about Translating Solitons in Semi Riemannian Manifolds. Moreover, we investigate those which are invariant by the action of a Lie group of isometries of the ambient space, by paying attention to the behaviour close to the singular orbit (if any) and at infinity. Then, we provide some related examples.