Topics in Lorentz Geometry

Ivo Terek

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arXiv · 1908.01710

Topics in Lorentz Geometry

Ivo Terek

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Abstract

Lecture notes from the mini-course "Topics in Lorentz Geometry" taught at the University of S\~{a}o Paulo, in March/2019. The text has three parts: (i) an overall view of linear algebra in the pseudo-Euclidean space $\mathbb{R}^n_\nu$, 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.

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Ivo Terek. 2019-08-02. Topics in Lorentz Geometry. https://arxiv.org/abs/1908.01710

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