Year: 2019
Type: preprint
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 $\mathbb{R}^n_ν$, 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.
Source: arXiv (Cornell University)
Author: Terek, Ivo
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G2808639341, G4402799499
OpenAlex ID: W2966842136