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001-es BibID:	BIBFORM103597
035-os BibID:	(cikkazonosító)19 (WOS)000523266000001 (Scopus)85083269057
Első szerző:	Vincze Csaba (matematikus)
Cím:	On the extremal compatible linear connection of a Randers space / Csaba Vincze, Márk Oláh
Dátum:	2020
ISSN:	0047-2468 1420-8997
Megjegyzések:	A linear connection on a Finsler manifold is called compatible to the metric if its parallel transports preserve the Finslerian length of tangent vectors. Generalized Berwald manifolds are Finsler manifolds equipped with a compatible linear connection. Since the compatibility to the Finslerian metric does not imply the unicity of the linear connection in general, the first step of checking the existence of compatible linear connections on a Finsler manifold is to choose the best one to look for. A reasonable choice is introduced in Vincze (J Differ Geom Appl, 2019. ) called the extremal compatible linear connection, which has torsion of minimal norm at each point. Randers metrics are special Finsler metrics that can be written as the sum of a Riemannian metric and a 1-form (they are "translates" of Riemannian metrics). In this paper, we investigate the compatibility equations for a linear connection to a Randers metric. Since a compatible linear connection is uniquely determined by its torsion, we transform the compatibility equations by taking the torsion components as variables. We determine when these equations have solutions, i.e. when the Randers space becomes a generalized Berwald space admitting a compatible linear connection. Describing all of them, we can select the extremal connection with the norm minimizing property. As a consequence, we obtain the characterization theorem in Vincze (Indag Math 26(2):363-379, 2014): a Randers space is a non-Riemannian generalized Berwald space if and only if the norm of the perturbating term with respect to the Riemannian part of the metric is a positive constant.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk Finsler spaces Generalized Berwald spaces Intrinsic geometry Randers spaces Extremal compatible linear connection
Megjelenés:	Journal of Geometry. - 111 : 2 (2020), p. 1-16. -
További szerzők:	Oláh Márk (1994-) (matematikus)
Pályázati támogatás:	EFOP-3.6.1-16-2016-00022 EFOP TKA-DAAD-307818 Egyéb
Internet cím:	Szerző által megadott URL DOI Intézményi repozitóriumban (DEA) tárolt változat
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