Affine connections in the Finsler space


Irena Čomić




In the Finsler space some general connection coefficients are introduced which depend on seven arbitrarily chosen parameters. Special cases of these are Cartan connection coefficients and some of the recurrent Finsler spaces. All of them have the property that the angle between two vectors by parallel displacement remains unchanged. It is shown that there are $2^7$ essentially different types of connection coefficients of this kind. For the general case some fundamental relations are obtained.