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001-es BibID:	BIBFORM107056
035-os BibID:	(WoS)000735772500001 (Scopus)85122061008
Első szerző:	Vincze Csaba (matematikus)
Cím:	On the extremal compatible linear connection of a generalized Berwald manifold / Csaba Vincze
Dátum:	2022
ISSN:	0001-9054 1420-8903
Megjegyzések:	Generalized Berwald manifolds are Finsler manifolds admitting linear connections such that the parallel transports preserve the Finslerian length of tangent vectors (compatibility condition). It is known (Vincze in J AMAPN 21:199-204, 2005) that such a linear connection must be metrical with respect to the averaged Riemannian metric given by integration of the Riemann-Finsler metric on the indicatrix hypersurfaces. Therefore the linear connection (preserving the Finslerian length of tangent vectors) is uniquely determined by its torsion. If the torsion is zero then we have a classical Berwald manifold. Otherwise, the torsion is some strange data we need to express in terms of the intrinsic quantities of the Finsler manifold. The paper presents the idea of the extremal compatible linear connection of a generalized Berwald manifold by minimizing the pointwise length of its torsion tensor. It is uniquely determined because the number of the Lagrange multipliers is equal to the number of the equations for the compatibility of the linear connection with the Finslerian metric. Using the reference element method, the extremal compatible linear connection can be expressed in terms of the canonical data as well. It is an intrinsic algorithm to check the existence of compatible linear connections on a Finsler manifold because it is equivalent to the existence of the extremal compatible linear connection.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk Finsler spaces Generalized Berwald spaces Intrinsic geometry
Megjelenés:	Aequationes Mathematicae. - 96 : 1 (2022), p. 53-70. -
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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