Geodesic Mappings of Equiaffine and Anti-Equiaffine General Affine Connection Spaces Preserving Torsion

Mića S. Stanković, Marija S. Ćirić, Milan Lj. Zlatanović

We consider equitorsion geodesic mappings of equiaffine spaces of the $\theta$-kind, $\theta\in \{0,...,5\}$. In the case when $\theta \in \{0,5\}$, vector $\psi_i$, which determines that mapping, is gradient, which doesn't hold in general case. We found the condition when the vector $\psi_i$ is gradient in the case of $\theta\in \{0,...,4\}$. Some invariant geometric objects of such mappings are found. Anti-equiaffine spaces of $\theta$-kind, $\theta \in \{0,5\}$ are introduced and discussed. Equitorsion geodesic mappings of such spaces are described and some invariants are found. Jozef Mikes 3100