On a special type of generalized Berwald manifolds: semi-symmetric linear connections preserving the Finslerian length of tangent vectors (Q1695712)

The author obtains new results on the theory of generalized Berwald manifolds. He also obtains new and interesting results on Asanov's Finsleroid-Finsler metrics. In this respect, the author characterizes this kind of metrics as the solution of a conformal rigidity problem and he proves that a Finsleroid-Finsler manifold is a Landsberg manifold (Unicorn), if and only if it is a generalized Berwald manifold with a semi-symmetric compatible linear connection.