Böcker av Barrett (University of California O'Neill

Intended for students who have completed the standard first courses in calculus and linear algebra, this edition provides an introduction to the geometry of curves and surfaces. It places emphasis on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard.

This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.