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

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 time-like, invariant translating solitons by rotations and boosts in Minkowski space.(1) the Spanish MICINN and ERDF, project PID2020-116126GB-I00; (2) the “Maria de Maeztu” Excellence Unit IMAG, ref. CEX2020-001105-M, funded by MCIN/AEI/10.13039/501100011033/; (3) Spanish FEDER-Andalucı́a grant PY20 01391; (4) open access charge: Universidad de Granada / CBUA