Eisenhart Riemannian Geometry

1. Auflage 2016
ISBN: 978-1-4008-8421-6
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 272 Seiten

Reihe: Princeton Landmarks in Mathematics and Physics

In his classic work of geometry, Euclid focused on the properties of flat surfaces. In the age of exploration, mapmakers such as Mercator had to concern themselves with the properties of spherical surfaces. The study of curved surfaces, or non-Euclidean geometry, flowered in the late nineteenth century, as mathematicians such as Riemann increasingly questioned Euclid's parallel postulate, and by relaxing this constraint derived a wealth of new results. These seemingly abstract properties found immediate application in physics upon Einstein's introduction of the general theory of relativity.

In this book, Eisenhart succinctly surveys the key concepts of Riemannian geometry, addressing mathematicians and theoretical physicists alike.

Autoren/Hrsg.

Eisenhart, Luther Pfahler

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie

Inhaltsverzeichnis

Frontmatter, pg. i
Preface, pg. v
Contents, pg. vii
Chapter I. Tensor analysis, pg. 1
Chapter II. Introduction of a metric, pg. 34
Chapter III. Orthogonal ennuples, pg. 96
Chapter IV. The geometry of sub-spaces, pg. 143
Chapter V. Sub-spaces of a flat space, pg. 187
Chapter VI. Groups of motions, pg. 221
Appendices, pg. 252
Bibliography, pg. 289
Index, pg. 301