Die Bedeutung von Christoffel für die Geometrie

Abstract

Since more than a century Christoffel’s name is irresolubly bound to Geometry. The famous Christoffel symbols occurred for the first time in a paper on the theory of invariants of a Riemannian metric. Nowadays, these symbols are used to describe a general linear connection in a vector bundle. The importance of this concept is amply demonstrated in the theory of relativity. All papers of Christoffel have a strong geometric flavor, and there are four which are dedicated to geometry proper. After a discussion of the contents of these papers we can place Christoffel right after Gauss and Riemann as one of the prime movers of differential geometry in the 19th century, in the same line with Beltrami, Weingarten, Bonnet and Darboux. We conclude with a discussion of the future rôle of geometry. The roots of geometry in the realm of natural intuition and physical phenomenon will be needed to yield the necessary strength of freeing modern mathematics from some of its degenerations. The work of Christoffel as one of the truly independent spirits in his generation can be an example to all of us today.