Relation between the minimal Lorentz surfaces in \mathbb R⁴₂ and \mathbb R³₁

2024/02/27 by Krasimir Kanchev, Kanchev, Krasimir, Ognian Kassabov +3
Mathematics · Physics and Astronomy · #53A10 #53A35 #53B25 (Secondary) #53B30 (Primary) #Advanced Differential Geometry Research #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2402.17850

openalex publication_date 2024/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give Weierstrass-type representation formulas for the null curves and for the minimal Lorentz surfaces in the Minkowski 3-space \mathbb R³₁ using real-valued functions. Applying the Weierstrass-type representations for the null curves, we find a correspondence between the null curves in \mathbb R⁴₂ and the pairs of null curves in \mathbb R³₁. Based on this correspondence, we obtain a relation between the minimal Lorentz surfaces in \mathbb R⁴₂ and the pairs of minimal Lorentz surfaces in \mathbb R³₁.

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