2016/07/15 by Lawn, Marie-Amelie, Ortega, Miguel
#53C21 #53C42 #53C44 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1607.04571
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.