Spaces with two affine connections

Abstract

In an n-dimensional space with several affine connections it is possible to define certain tensors analogous to the ordinary curvature tensor. They may be obtained as coefficients of the generalized Ricci identities of the classical Riemannian geometry, as was done by the present author in a previous paper (Santaló, 1954). Recently, following a similar way, Sen (Sen, 1964) has obtained new tensors and new quantities, which he applies to get generalized forms of the equations of the unified field theory of Einstein, as developed by Hlavaty (Hlavaty, 1957). In the present paper we consider especially the case of two connections aT, bT and obtain several tensors (among them those of Sen) and certain properties of these tensors