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arXiv · 2211.14529

New Examples of Translating Solitons in Generalised Robertson-Walker Geometries

Diego Artacho·Marie-Amélie Lawn·Miguel Ortega
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Abstract

Translators can be regarded as submanifolds which satisfy the mean curvature flow equation when evolving by translations along a distinguished vector field of the ambient space. We study translators in Generalised Robertson-Walker spacetimes, due to their importance as Lorentzian manifolds, and because they admit a natural conformal Killing timelike vector field carrying substantial geometric information, which will play the role of this translating vector field. We identify three one-parameter families of warping functions for which these objects exist. As a first example of this notion of translator, we classify the analogues of the classical Grim Reapers within this context.

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Diego Artacho, Marie-Amélie Lawn, Miguel Ortega. 2022-11-26. New Examples of Translating Solitons in Generalised Robertson-Walker Geometries. https://doi.org/10.4310/ajm.260122040802

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