**Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 16, pp. 33-63 (2000)
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A new look at Finsler connections and special Finsler manifolds

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József Szilasi and Csaba Vincze

J. Szilasi: Institute of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, Pf. 12, Hungary, szilasi@math.klte.hu; Cs. Vincze: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, H-1364 Budapest, Pf. 127, Hungary, csvincze@math.klte.hu.

**Abstract:** Continuing Grifone's pioneering work, we present a systematic treatment of some distinguished Finsler connections and some special Finsler manifolds, built on three pillars: the theory of horizontal endomorphisms, the calculus of vector-valued forms and a "tangent bundle version" of the method of moving frames.

**Keywords:** Horizontal endomorphisms; Cartan tensors; Berwald connection, Cartan connection, Chern-Rund connection; Berwald manifold; locally Minkowski manifold.

**Classification (MSC91):** 53C07; 53C60

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