Classical differential geometry with Christoffel symbols of Ehresmann \varepsilon-connections

Ercument Ortacgil

Address. Bogazici University, Mathematics Department, Bebek, Istanbul 80815, Turkiye

E-mail: ortacgil@boun.edu.tr

Abstract. We give a method based on an idea of O. Veblen which gives explicit formulas for the covariant derivatives of natural objects in terms of the Christoffel symbols of a symmetric Ehresmann $\varepsilon$-connection.

AMSclassification. 53A55, 53C05

Keywords. Covariant differentiation, Christoffel symbols