Couto I. Introduction to Lorentz Geometry. Curves and Surfaces 2021

Textbook in PDF format

Lorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity. Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe, such as: What is the shape of the universe ? What is a spacetime ? What is the relation between gravity and curvature ? Why exactly is time treated in a different manner than other spatial dimensions ?
Introduction to Lorentz Geometry: Curves and Surfaces intends to provide the reader with the minimum mathematical background needed to pursue these very interesting questions, by presenting the classical theory of curves and surfaces in both Euclidean and Lorentzian ambient spaces simultaneously.
Welcome to Lorentz-Minkowski Space.
Local Theory of Curves.
Surfaces in Space.
Abstract Surfaces and Further Topics.
Some Results from Differential Calculus