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001-es BibID:	BIBFORM106863
035-os BibID:	(WoS)000854852000001 (Scopus)85138276990 (cikkazonosító)45
Első szerző:	Vincze Csaba (matematikus)
Cím:	Finsler metrics and semi-symmetric compatible linear connections / Csaba Vincze, Márk Oláh
Dátum:	2022
ISSN:	0047-2468 1420-8997
Megjegyzések:	Finsler metrics are direct generalizations of Riemannian metrics such that the quadratic Riemannian indicatrices in the tangent spaces of a manifold are replaced by more general convex bodies as unit spheres. A linear connection on the base manifold is called compatible with the Finsler metric if the induced parallel transports preserve the Finslerian length of tangent vectors. Finsler manifolds admitting compatible linear connections are called generalized Berwald manifolds Wagner (Dokl Acad Sci USSR (N.S.) 39:3-5, 1943). Compatible linear connections are the solutions of the so-called compatibility equations containing the components of the torsion tensor as unknown quantities. Although there are some theoretical results for the solvability of the compatibility equations (monochromatic Finsler metrics Bartelmeß and Matveev (J Diff Geom Appl 58:264-271, 2018), extremal compatible linear connections and algorithmic solutions Vincze (Aequat Math 96:53-70, 2022)), it is very hard to solve them in general because compatible linear connections may or may not exist on a Finsler manifold and may or may not be unique. Therefore special cases are of special interest. One of them is the case of the socalled semi-symmetric compatible linear connection with decomposable torsion tensor. It is proved Vincze (Publ Math Debrecen 83(4):741-755, 2013 (see also Vincze (Euro J Math 3:1098-1171, 2017))) that such a compatible linear connection must be uniquely determined. The original proof is based on averaging in the sense that the 1-form in the decomposition of the torsion tensor can be expressed by integrating differential forms on the tangent manifold over the Finslerian indicatrices. The integral formulas are very difficult to compute in practice. In what follows we present a new proof for the uniqueness by using linear algebra and some basic facts about convex bodies. We present an explicit formula for the solution without integration. The method has a new contribution to the problem as well: necessary conditions of the solvability are formulated in terms of intrinsic equations without unknown quantities.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk Convex bodies Tangent hyperplanes Minkowski norm Finsler spaces Generalized Berwald spaces Semi-symmetric linear connections Intrinsic Geometry
Megjelenés:	Journal of Geometry. - 113 : 3 (2022), p. 1-14. -
További szerzők:	Oláh Márk (1994-) (matematikus)
Pályázati támogatás:	ÚNKP-21-3 Egyéb
Internet cím:	Szerző által megadott URL DOI Intézményi repozitóriumban (DEA) tárolt változat
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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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001-es BibID:	BIBFORM102754
035-os BibID:	(Scopus)85072748598
Első szerző:	Vincze Csaba (matematikus)
Cím:	On generalized Berwald surfaces with locally symmetric fourth root metrics / Cs. Vincze, T. R. Khoshdani, M. Olah
Dátum:	2019
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk
Megjelenés:	Balkan Journal of Geometry and Its Applications. - 24 : 2 (2019), p. 63-78. -
További szerzők:	Khoshdani, Tahere Reza (matematikus) Oláh Márk (1994-) (matematikus)
Pályázati támogatás:	UNKP-18-2 Egyéb EFOP-3.6.1-16-2016-00022 EFOP
Internet cím:	Szerző által megadott URL Intézményi repozitóriumban (DEA) tárolt változat
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