Rotational K^alpha-translators in Minkowski space

Abstract

A spacelike surface in Minkowski space R31 is called a Kα-translator of the flow by the powers of Gauss curvature if satisfies Kα=⟨N,⃗v⟩, α≠0, where K is the Gauss curvature, N is the unit normal vector field and ⃗v is a direction of R31. In this paper, we classify all rotational Kα-translators. This classification will depend on the causal character of the rotation axis. Although the theory of the Kα-flow holds for spacelike surfaces, the equation describing Kα-translators is still valid for timelike surfaces. So we also investigate the timelike rotational surfaces that satisfy the same prescribing Gauss curvature equation.