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arXiv · 1607.04571

Translating solitons from semi-Riemannian foliations

Marie-Amelie Lawn·Miguel Ortega
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Abstract

We recall the notion of (vertical) translating solitons in a product of a semi-Riemannian manifold $(M,g)$ and the real line. Mainly, we restrict our attention to those which are the graph of a smooth function. When dealing with submersions, we show a criteria to lift (or project) translating solitons from the base manifold to the total space (or viceversa). In particular, manifolds foliated by codimension 1 orbits of a Lie group action give rise to such solitons, up to solving a first-order ordinary differential equation. This gives us explicit criteria under which the graph of a function is a soliton, and we employ them to construct many examples of solitons, both new and old, in a unified way.

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Marie-Amelie Lawn, Miguel Ortega. 2016-07-15. Translating solitons from semi-Riemannian foliations. https://arxiv.org/abs/1607.04571

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