3 Ergebnisse.

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 towa...

Suitable for advanced undergraduates and graduate students of mathematics as well as for physicists, this unique monograph and self-contained treatment constitutes an introduction to modern techniques in differential geometry. 1995 edition.

This edition maintains the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis is placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard. A thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises are inclu...