Translating solitons in arbitrary codimension
Mean curvature flow has finite-time singularities in general which are classified into two categories: Type I and Type II. It is known that by rescaling at a singularity, we obtain a self-shrinker as a limiting submanifold of Type I and an eternal solution as a limiting submanifold of Type II. Translating solitons are important examples of eternal solutions, which do not change their shape under the mean curvature flow up to translation in Euclidean space. Although many authors study translating solitons in codimension one, there are few references and examples for higher-codimensional cases except for Lagrangian translating solitons. In this paper, the author first observes non-trivial examples of translating solitons in arbitrary codimension. Inspired by the fact that they have the property called parallel principal normal and the work of \textit{K. Smoczyk} for self-shrinkers in [Int. Math. Res. Not. 2005, No. 48, 2983--3004 (2005; Zbl 1085.53059)], the author characterizes the complete translating solitons with the above property.
scientific article; zbMATH DE number 6837105