Rotational K^α-translators in Minkowski space

2022/02/12 by Muhittin Evren Aydın, Aydin, Muhittin Evren, Rafael López +1
Mathematics · Physics and Astronomy · #35J96 #53A15 #53C44 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2202.06131

openalex publication_date 2022/02/12 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

A spacelike surface in Minkowski space ℝ₁³ is called a K^α-translator of the flow by the powers of Gauss curvature if satisfies K^α= ⟨ N,v⟩, α≠ 0, where K is the Gauss curvature, N is the unit normal vector field and v is a direction of ℝ₁³. In this paper, we classify all rotational K^α-translators. This classification will depend on the causal character of the rotation axis. Although the theory of the K^α-flow holds for spacelike surfaces, the equation describing K^α-translators is still valid for timelike surfaces. So we also investigate the timelike rotational surfaces that satisfy the same prescribing Gauss curvature equation.

Related

• Translators of the Gauss curvature flow
• Invariant λ-translators in Lorentz-Minkowski space
• K^α-translators of offset surfaces
• Invariant λ-translators for the Gauss curvature flow in Euclidean space
• Rotational surfaces in a 3-dimensional normed space