Abstract
In Chap. 5, before exposing the long and exciting history of Lie group discovery, we remarked that differential geometry is at the basis not only of General Relativity but of all those Gauge Theories by means of which XXth century Physics obtained a consistent and experimentally verified description of all Fundamental Interactions.
My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful....
Hermann Weyl
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
A manifold (defined in this section) is named affine when it is also a vector space.
- 2.
The translation of Riemann’s essay from German into English was done by William Clifford.
- 3.
In the original German text of Riemann these were named mehrfach ausgedehnter Grossen. In modern scientific German the notion of manifolds is referred to as mannigfaltigkeiten.
- 4.
Einfachsten Thatsachen in the original German text.
- 5.
He gave to science Absolute Differential Calculus, essential instrument of the Theory of General Relativity, a new vision of the Universe.
- 6.
The fundamental notion of fibre bundle is described in simple words in Sect. 7.4
- 7.
The very first embryonal idea of the Ricci tensor actually appeared as early as 1892 in another publication of its inventor [150].
- 8.
Ludwig Maurer (1859–1927) obtained his Doctorate in 1887 from the University of Strassburg (at the time under German rule after the defeat of France in the 1870 war) and became professor of Mathematics at the University of Tübingen. His doctoral dissertation Zur Theorie der linearen Substitutionen [142] happens to contain a germ of the idea of Maurer–Cartan forms developed by Cartan in 1904.
- 9.
About the functions which help determining the attraction of general spheroids. Programme for a thesis about some properties of curves with a double curvature.
- 10.
Obviously Maxwell was not aware of the mathematical significance of the vector potential \(\mathbf {A}\), yet that \(\mathbf {A}\) is a \(\mathrm {U(1)}\)–connection, is a fact beyond any doubt.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Fré, P.G. (2018). A Short History of Differential Geometry. In: A Conceptual History of Space and Symmetry . Springer, Cham. https://doi.org/10.1007/978-3-319-98023-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-98023-2_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-98022-5
Online ISBN: 978-3-319-98023-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)