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On a special type of generalized Berwald manifolds: semi-symmetric linear connections preserving the Finslerian length of tangent vectors. (English) Zbl 1384.53024

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.

MSC:

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C65 Integral geometry
52A21 Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry)
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