Ruled translating solitons in Minkowski 3-space

TL;DR

This paper classifies all ruled translating solitons in Minkowski 3-space, revealing unique non-cylindrical solutions and extending the understanding of such surfaces beyond Euclidean analogs.

Contribution

It provides a complete classification of ruled translating solitons in Minkowski 3-space, including non-cylindrical examples and their geometric properties.

Findings

Existence of non-cylindrical ruled translating solitons in Minkowski space.

Classification of cylindrical translating solitons analogous to Euclidean grim reapers.

Identification of lightlike ruling vectors leading to new soliton solutions.

Abstract

We characterize all ruled translating solitons in Minkowski 3-space. In contrast to the Euclidean space, we find ruled translating solitons that are not cylindrical. These surfaces appear when the vector field that defines the rulings, viewed as a curve, is a lightlike straight line. We also classify all cylindrical translating solitons, obtaining surfaces that can be considered as analogous to the grim reapers of Euclidean space, but also other surfaces which have no a counterpart in the Euclidean space.