Topics in Lorentz Geometry

2019/08/02 by Ivo Terek, Terek, Ivo
Mathematics · #53-01 #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #math.DG #msc:53-01

paper · pdf · doi:10.48550/arxiv.1908.01710

76 pages, 23 figures

openalex publication_date 2019/08/02 · arxiv created 2019/09/02 · arxiv updated 2019/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Lecture notes from the mini-course "Topics in Lorentz Geometry" taught at the University of São Paulo, in March/2019. The text has three parts: (i) an overall view of linear algebra in the pseudo-Euclidean space ℝⁿ_ν, with focus on Lorentz-Minkowski space and its role in Physics; (ii) a version of the Fundamental Theorem of Curves in 3-dimensional Lorentz-Minkowski space, with adaptations to curves with degenerate osculating plane; (iii) the problem of the diagonalization of the Weingarten map for timelike surfaces, local classification of surfaces with constant Gaussian curvature K and Weierstrass' representation formula in Lorentz-Minkowski space (using split-complex algebra). V2: added references.

Related

• Global Lorentzian Geometry
• Relation between the minimal Lorentz surfaces in \mathbb R⁴₂ and \mathbb R³₁
• Curves in Lorentz-Minkowski plane with curvature depending on their position
• Rotational Weingarten surfaces in Lorentz-Minkowski space
• On the History of Geometrization of Space-time: From Minkowski to Finsler Geometry