On generalized Berwald manifolds: extremal compatible linear connections, spe-cial metrics and low dimensional spaces

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Vincze Csaba

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Journal Paper

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Journal: AUT Journal of Mathematics and Computing Year:2021 | Volume:2 | Issue:2 Page(s): 213-237

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Title

On generalized Berwald manifolds: extremal compatible linear connections, spe-cial metrics and low dimensional spaces

Author(s)

Vincze Csaba | Issue Writer Certificate

Keywords

Averaging

Riemann-Finsler Geometry

Generalized Berwald

manifolds

Abstract

The notion of Generalized Berwald manifolds goes back to V. Wagner [60]. They are Finsler manifolds admitting linear connections on the base manifold such that the parallel transports preserve the Finslerian length of tangent vectors (compatibility condition). Presenting a panoramic view of the general theory we are going to summarize some special problems and results. Spaces of special metrics are of special interest in the Generalized Berwald manifold theory. We discuss the case of Generalized Berwald Randers metrics, Finsler surfaces and Finsler manifolds of dimension three. To provide the unicity of the compatible linear connection we are looking for, we introduce the notion of the extremal compatible linear connection minimizing the norm of the torsion tensor point by point. The mathematical formulation is given in terms of a conditional extremum problem for checking the existence of compatible linear connections in general. Explicite computations are presented in the special case of Generalized Berwald Randers metrics.

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APA: Copy

Vincze, Csaba. (2021). On generalized Berwald manifolds: extremal compatible linear connections, spe-cial metrics and low dimensional spaces. AUT JOURNAL OF MATHEMATICS AND COMPUTING, 2(2), 213-237. SID. https://sid.ir/paper/1043876/en

Vancouver: Copy

Vincze Csaba. On generalized Berwald manifolds: extremal compatible linear connections, spe-cial metrics and low dimensional spaces. AUT JOURNAL OF MATHEMATICS AND COMPUTING[Internet]. 2021;2(2):213-237. Available from: https://sid.ir/paper/1043876/en

IEEE: Copy

Csaba Vincze, “On generalized Berwald manifolds: extremal compatible linear connections, spe-cial metrics and low dimensional spaces,” AUT JOURNAL OF MATHEMATICS AND COMPUTING, vol. 2, no. 2, pp. 213–237, 2021, [Online]. Available: https://sid.ir/paper/1043876/en

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