Finsler metrics and semi-symmetric compatible linear connections

Abstract Finsler metrics are direct generalizations of Riemannian such that the quadratic indicatrices in tangent spaces a manifold replaced by more general convex bodies as unit spheres. A linear connection on base is called compatible with metric if induced parallel transports preserve Finslerian length vectors. manifolds admitting connections generalized Berwald Wagner (Dokl Acad Sci USSR (N.S.) 39:3–5, 1943). Compatible solutions so-called compatibility equations containing components torsion tensor unknown quantities. Although there some theoretical results for solvability (monochromatic Bartelmeß and Matveev (J Diff Geom Appl 58:264–271, 2018), extremal algorithmic Vincze (Aequat Math 96:53–70, 2022)), it very hard to solve them because may or not exist be unique. Therefore special cases interest. One case semi-symmetric decomposable tensor. It proved (Publ Debrecen 83(4):741–755, 2013 (see also (Euro J 3:1098–1171, 2017))) must uniquely determined. The original proof based averaging sense 1-form decomposition can expressed integrating differential forms over indicatrices. integral formulas difficult compute practice. In what follows we present new uniqueness using algebra basic facts about bodies. We an explicit formula solution without integration. method has contribution problem well: necessary conditions formulated terms intrinsic