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001-es BibID:	BIBFORM129066
Első szerző:	Oláh Márk (matematikus)
Cím:	Non-transitive subgroups of co-rank one in the orthogonal group / Márk Oláh, Myroslav Stoika, Csaba Vincze
Dátum:	2025
ISSN:	0033-3883 2064-2849
Megjegyzések:	It is known that any non-transitive closed subgroup G in the orthogonal group is remetrizable by a non-Euclidean Minkowski functional keeping the elements in G as linear isometries. Minkowski geometry is an alternative of Euclidean geometry for G. To measure the non-transitivity of the subgroup in the orthogonal group, we can use the Hausdorff distance between the Euclidean unit sphere and the orbit of a Euclidean unit element under G. The so-called flat subspace is spanned by the configuration of elements where the Hausdorff distance is attained at. Taking the maximum of the dimension of flat subspaces, we have the rank of the group G. It is known that subgroups of maximal rank are finite or reducible. They are natural prototypes of non-transitive subgroups in the orthogonal group. In the paper, we are going to investigate non-transitive subgroups of rank n?1 (co-rank one). We prove that the unit component G^0 ? G must be an Abelian subgroup in the special orthogonal group, and the elements in G can be described in terms of subspaces given by simultaneous quasi-diagonalization in G^0. Independently of the rank condition, applications of simultaneous quasi-diagonalization are also presented for one- and two-dimensional non-transitive closed subgroups.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény hazai lapban folyóiratcikk orthogonal group non-transitive subgroups orbits Hausdorff distance
Megjelenés:	Publicationes Mathematicae Debrecen. - 106 : 3-4 (2025), p.265-283. -
További szerzők:	Stoika, Myroslav (Mathematics) Vincze Csaba (1971-) (matematikus)
Pályázati támogatás:	HUN-REN Hungarian Research Network Egyéb 84/37/2022/HTMT
Internet cím:	DOI Intézményi repozitóriumban (DEA) tárolt változat
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001-es BibID:	BIBFORM107055
035-os BibID:	(WoS)000798248100005 (Scopus)85138585898
Első szerző:	Vincze Csaba (matematikus)
Cím:	On generalized Berwald manifolds of dimension three / Csaba Vincze, Mark Olah
Dátum:	2022
ISSN:	0033-3883 2064-2849
Megjegyzések:	A linear connection on a Finsler manifold is called compatible with the Finsler function if its parallel transports preserve the Finslerian length of tangent vectors. Generalized Berwald manifolds are Finsler manifolds equipped with a compatible linear connection. In the paper, we present a general and intrinsic method to characterize the compatible linear connections on a Finsler manifold of dimension three. We prove that if a compatible linear connection is not unique, then the indicatrices must be Euclidean surfaces of revolution. The surplus freedom of choosing compatible linear connections is related to Euclidean symmetries. The unicity of the solution of the compatibility equations can be provided by some additional requirements. Following the idea in [11], we are also looking for the so-called extremal compatible linear connection minimizing the norm of its torsion at each point of the manifold.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény hazai lapban folyóiratcikk Finsler spaces generalized Berwald spaces intrinsic geometry extremal compatible linear connections
Megjelenés:	Publicationes Mathematicae Debrecen. - 100 : 3-4 (2022), p. 337-363. -
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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