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5 - Riemannian Geometry

Published online by Cambridge University Press:  08 December 2022

Esko Keski-Vakkuri ,
Claus Montonen  and
Marco Panero
Esko Keski-Vakkuri
Affiliation:
University of Helsinki
Claus Montonen
Affiliation:
University of Helsinki
Marco Panero
Affiliation:
Università degli Studi di Torino, Italy
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Summary

We equip differentiable manifolds with a metric and introduce differential geometry, which provides the mathematical formalism underlying the theory of general relativity and many other applications in different areas of physics, science, and engineering.

Keywords

Riemannian geometrymetric tensorparallel transportcovariant derivativegeodesicscurvatureisometries
Type
Chapter
Information
Mathematical Methods for Physics
An Introduction to Group Theory, Topology and Geometry
 , pp. 170 - 232
Publisher: Cambridge University Press
Print publication year: 2022

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