Rotational K-alpha-translators in Minkowski Space

A spacelike surface in Minkowski space R31 is called a Ka-translator of the flow by the powers of Gauss curvature if satisfies Ka =< N,v(->)>, alpha not equal 0, where K is the Gauss curvature, N is the unit normal vector field and.v is a direction of R-1(3). In this paper, we classify all rotational K-alpha-translators. This classification will depend on the causal character of the rotation axis. Although the theory of the Ka-flow holds for spacelike surfaces, the equation describing K-alpha-translators is still valid for timelike surfaces. So we also investigate the timelike rotational surfaces that satisfy the same prescribing Gauss curvature equation.

Automated summary

In this paper, we study Ka-translators, which are spacelike surfaces in Minkowski space R31 that satisfy the equation Ka =< N,v(->)> with alpha not equal to 0. We classify all rotational K-alpha-translators based on the causal character of the rotation axis. Additionally, we investigate timelike rotational surfaces that satisfy the same prescribing Gauss curvature equation, although the theory of the Ka-flow is applicable to spacelike surfaces.