Questions tagged [differential-geometry]

For questions about the discipline that uses differential calculus and linear algebra to study geometrical problems.

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26
votes
2answers
1k views

When and how was the geometric understanding of gauge theories developed?

In theoretical physics, the modern perspective on gauge theory is that it is most elegantly described in the 'language' of differential geometry. I am interested in the history behind these ideas. ...
18
votes
3answers
1k views

What was the motivation for the development of modern, intrinsic, differential geometry?

I know that tensor calculus was developed around the same time as general relativity. Tensor calculus was the prime way to deal with geometric objects, based on expliciting all coordinates and doing ...
9
votes
2answers
962 views

Motivation behind Euler Theorem in differential geometry

I am teaching a class on elementary differential geometry and I would like to know, for myself and for my students, something more about the history of Euler Theorem and Euler equation: the curvature ...
18
votes
1answer
2k views

How was Einstein led to make a contact with Differential Geometry for his theory of General Relativity?

General Relativity was developed with Differential Geometry as the tool. How was Einstein led to make a contact with Differential Geometry for his theory of General Relativity? Who suggested him to ...
8
votes
1answer
699 views

How was curvature originally defined and calculated?

I am interested in the early history of curvature. Who defined it first and when, who came up with the name, how was it calculated before mathematicians used calculus to define $k=|α''(s)|$? Are there ...
7
votes
1answer
780 views

How did the exponential map of Riemannian geometry get its name?

I've read in several books, including Milnor's Morse Theory and Petersen's Riemannian Geometry, that the exponential map in Riemannian geometry is named so because it agrees with the exponential map ...
9
votes
4answers
628 views

Help translate from German a quote by Hermann Weyl in Space Time Matter

I would like to find an accurate translation to the following quote from Space Time Matter: Man muß gegen diese Orgien des Formalismus, mit dem man heute sogar die Techniker zu belästigen beginnt, ...
7
votes
2answers
367 views

Where did Cartan introduce his notation for basis vectors and covectors?

There is a notation used in differential geometry and general relativity in which the partial derivative operators $\partial_\mu$ are used as the basis for the space of contravariant vectors, and ...
6
votes
2answers
475 views

The origin of the name “connection” in differential geometry

Everyone will encounter the notion of connection in differential geometry. But who gave this name of connection( or affine connection)? Why is this derivative operator called connection? What object ...
5
votes
1answer
262 views

Did Gauss formulate, or at least know of, the full essence of the Gauss-Bonnet Theorem?

I know that a special case of the Bonnet theorem, called the Theorema Elegantissimum, was proved by Gauss in his 1827 treatise on differential geometry. This was a theroem that dealt with the ...
4
votes
3answers
685 views

History of the derivative/tangent of a curve

I just want to know the history of the derivative. Whenever I Google for it, I find the history of calculus or the tangent of a curve. However, they barely touch upon what happened before Leibniz and ...
1
vote
1answer
170 views

Debauches of indices: Translation request

Finally I found the source of the dictum "debauches of indices". It is most often used in singular, as in Spivaks's Vol.II p.211. The original is from the first preface in E. Cartan's "Lecons sur la ...