MMN-1405
Ricci coefficients of rotation of generalized Finsler spaces
Abstract
On a differentiable $N$-dimensional manifold a generalized Finsler space $GF_N$, as a metric space with non-symmetric
basic tensor $g_{ij}(x,\dot{x})$ is defined, under condition (\ref{1.4}).
Using the basic tensor, by (\ref{1.15,1.16}) a non-symmetric connection $P^*$ is defined,
and also four kinds of covariant derivative in the Round's sense and five curvature tensors are obtained (\S1).
In the \S2 two kinds of Ricci coefficients of rotation are
defined and their properties are exposed. Also, integrability conditions of the equation expressing
covariant derivatives of the congruence vector by means of coefficients of rotation, are obtained.
At the \S3 a geodesic mapping of two spaces $GF_N$ and $G\overline{F}_N$ is defined
and some its properties are proved.
In the \S4 some invariants of such mappings in relation with the coefficients of rotation are studied.
Vol. 16 (2015), No. 2, pp. 1025-1039
DOI: 10.18514/MMN.2015.1405