Translating solitons from semi-Riemannian foliations

• DOI: 10.48550/arxiv.1607.04571
• Publication Date: 2016-01-01
• Authors: Marie-Amélie Lawn; Miguel Ortega‐Sán...
• Keywords: Codimension; Manifold (fluid mechanics); Lift (data mining); Riemannian manifold

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