christoffel

Christoffel is a surname of Germanic origin, derived from the given name Christoph through a diminutive or patronymic form. It is found in German- and Dutch-speaking regions and is borne by people in various fields. The most prominent scholarly bearer is the German mathematician Elwin Bruno Christoffel (1829–1900), whose work in differential geometry led to several mathematical concepts that carry his name.

In mathematics, Christoffel symbols are connection coefficients that describe how coordinate bases change under parallel transport on a curved manifold. There are Christoffel symbols of the first kind, Γijk, and of the second kind, Γi jk, related by the metric tensor. They appear in formulas for covariant differentiation and in the geodesic equations, encoding information about the manifold’s curvature and the chosen coordinate system.

Other concepts named after Christoffel include the Christoffel function, used in approximation theory and the study of orthogonal polynomials; the Christoffel-Darboux formula, which provides a concise expression for sums of orthogonal polynomials; and the Christoffel equation, important in the theory of elastic wave propagation in anisotropic media. These ideas reflect Christoffel’s influence across areas of geometry, analysis, and applied mathematics.

Because Christoffel is also a family name, the term may refer to individuals with this surname in various disciplines. In context, it often denotes mathematical constructs associated with Elwin Bruno Christoffel or, more broadly, works derived from his contributions.