2024/02/11 by Antonio Bueno, Bueno, Antonio, Irene Ortiz +1
Physics and Astronomy · #34C05 #34C40 #53A10 #53C42 #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2402.07237
openalex publication_date 2024/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given λ∈ℝ and v∈\mathbbL3, a λ-translator with velocity v is an immersed surface in \mathbbL3 whose mean curvature satisfies H=⟨ N,v⟩+λ, where N is a unit normal vector field. When λ=0, we fall into the class of translating solitons of the mean curvature flow. In this paper we study λ-translators in \mathbbL3 that are invariant under a 1-parameter group of translations and rotations. The former are cylindrical surfaces and explicit parametrizations are found, distinguishing on the causality of both the ruling direction and the λ-translators. In the case of rotational λ-translators we distinguish between spacelike and timelike rotations and exhibit the qualitative properties of rotational λ-translators by analyzing the non-linear autonomous system fulfilled by the coordinate functions of the generating curves.