Almost All Finsler Metrics have Infinite Dimensional Holonomy Group
We show that the set of Finsler metrics on a manifold contains an open everywhere dense subset of Finsler metrics with infinite-dimensional holonomy groups.
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| Published in: | The Journal of geometric analysis Vol. 31; no. 6; pp. 6067 - 6079 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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01-06-2021
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| Abstract | We show that the set of Finsler metrics on a manifold contains an open everywhere dense subset of Finsler metrics with infinite-dimensional holonomy groups. |
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| AbstractList | We show that the set of Finsler metrics on a manifold contains an open everywhere dense subset of Finsler metrics with infinite-dimensional holonomy groups. |
| Author | Matveev, V. S. Muzsnay, Z. Hubicska, B. |
| Author_xml | – sequence: 1 givenname: B. surname: Hubicska fullname: Hubicska, B. organization: University of Debrecen, Institute of Mathematics – sequence: 2 givenname: V. S. orcidid: 0000-0002-2237-1422 surname: Matveev fullname: Matveev, V. S. organization: Friedrich-Schiller-Universität, Institut für Mathematik – sequence: 3 givenname: Z. orcidid: 0000-0003-4516-7261 surname: Muzsnay fullname: Muzsnay, Z. email: muzsnay@science.unideb.hu organization: University of Debrecen, Institute of Mathematics |
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| Copyright | The Author(s) 2020 The Author(s) 2020. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| Keywords | 17B66 Finsler geometry 53B40 Holonomy 22E65 Curvature Algebras of vector fields 53C29 |
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| References | Matveev (CR11) 2009; 14 Kozma (CR10) 2000; 62 Vincze (CR22) 2005; 21 Chern, Shen (CR4) 2005 Borel, Lichnerowicz (CR3) 1952; 234 CR5 CR19 Szabó (CR21) 1981; 35 CR17 Muzsnay, Nagy (CR16) 2015; 39 Kolar, Michor, Slovak (CR9) 1993 Matveev (CR14) 2012; 62 Berger (CR1) 1955; 83 Muzsnay, Nagy (CR15) 2015; 27 Matveev, Troyanov (CR13) 2012; 16 Hubicska, Muzsnay (CR7) 2020; 30 Hubicska, Muzsnay (CR6) 2020; 73 Matveev (CR12) 2009; 74 Simons (CR20) 1962; 76 Ivanov, Lytchak (CR8) 2019; 94 Berwald (CR2) 1926; 25 Pontryagin (CR18) 1966 S-S Chern (517_CR4) 2005 B Hubicska (517_CR7) 2020; 30 B Hubicska (517_CR6) 2020; 73 VS Matveev (517_CR14) 2012; 62 L Berwald (517_CR2) 1926; 25 S Ivanov (517_CR8) 2019; 94 ZI Szabó (517_CR21) 1981; 35 I Kolar (517_CR9) 1993 J Simons (517_CR20) 1962; 76 VS Matveev (517_CR11) 2009; 14 VS Matveev (517_CR12) 2009; 74 LS Pontryagin (517_CR18) 1966 A Borel (517_CR3) 1952; 234 M Berger (517_CR1) 1955; 83 CS Vincze (517_CR22) 2005; 21 L Kozma (517_CR10) 2000; 62 VS Matveev (517_CR13) 2012; 16 517_CR5 Z Muzsnay (517_CR15) 2015; 27 517_CR17 Z Muzsnay (517_CR16) 2015; 39 517_CR19 |
| References_xml | – volume: 234 start-page: 1835 year: 1952 end-page: 1837 ident: CR3 article-title: Groupes d’holonomie des variétés riemanniennes publication-title: C. R. Acad. Sci. Paris contributor: fullname: Lichnerowicz – volume: 21 start-page: 199 year: 2005 end-page: 204 ident: CR22 article-title: A new proof of Szabó’s theorem on the Riemann metrizability of Berwald manifolds publication-title: Acta Math. Acad. Paedagog. Nyhazi contributor: fullname: Vincze – ident: CR19 – volume: 83 start-page: 279 year: 1955 end-page: 330 ident: CR1 article-title: Sur les groupes d’holonomie homogène des variétés à connexion affine et des variétés riemanniennes publication-title: Bull. Soc. Math. Fr. doi: 10.24033/bsmf.1464 contributor: fullname: Berger – volume: 74 start-page: 405 year: 2009 end-page: 416 ident: CR12 article-title: Riemannian metrics having common geodesics with Berwald metrics publication-title: Publ. Math. 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Structure theorems on Berwald spaces publication-title: Tensor contributor: fullname: Szabó – volume: 30 start-page: 107 year: 2020 end-page: 123 ident: CR7 article-title: Tangent Lie Algebra of a Diffeomorphism Group and Application to Holonomy Theory publication-title: J. Geom. Anal. doi: 10.1007/s12220-018-00138-3 contributor: fullname: Muzsnay – ident: CR5 – volume: 27 start-page: 767 year: 2015 end-page: 786 ident: CR15 article-title: Projectively flat Finsler manifolds with infinite dimensional holonomy publication-title: Forum Math. doi: 10.1515/forum-2012-0008 contributor: fullname: Nagy – volume: 62 start-page: 87 year: 2000 end-page: 90 ident: CR10 article-title: On holonomy groups of Landsberg manifolds publication-title: Tensor contributor: fullname: Kozma – volume-title: Riemann-Finsler geometry year: 2005 ident: 517_CR4 doi: 10.1142/5263 contributor: fullname: S-S Chern – volume: 62 start-page: 87 year: 2000 ident: 517_CR10 publication-title: Tensor contributor: fullname: L Kozma – ident: 517_CR17 doi: 10.1017/CBO9780511609565 – ident: 517_CR19 – volume: 25 start-page: 40 year: 1926 ident: 517_CR2 publication-title: Math. Z. doi: 10.1007/BF01283825 contributor: fullname: L Berwald – volume-title: Natural Operations in Differential Geometry year: 1993 ident: 517_CR9 doi: 10.1007/978-3-662-02950-3 contributor: fullname: I Kolar – volume-title: Nepreryvnye Gruppy. Translation: Topological Groups year: 1966 ident: 517_CR18 contributor: fullname: LS Pontryagin – ident: 517_CR5 – volume: 30 start-page: 107 year: 2020 ident: 517_CR7 publication-title: J. Geom. Anal. doi: 10.1007/s12220-018-00138-3 contributor: fullname: B Hubicska – volume: 21 start-page: 199 year: 2005 ident: 517_CR22 publication-title: Acta Math. Acad. Paedagog. Nyhazi contributor: fullname: CS Vincze – volume: 76 start-page: 213 year: 1962 ident: 517_CR20 publication-title: Ann. Math. doi: 10.2307/1970273 contributor: fullname: J Simons – volume: 39 start-page: 1 year: 2015 ident: 517_CR16 publication-title: Diff. Geom. Appl. doi: 10.1016/j.difgeo.2015.01.001 contributor: fullname: Z Muzsnay – volume: 94 start-page: 855 year: 2019 ident: 517_CR8 publication-title: Comment. Math. Helv. doi: 10.4171/CMH/476 contributor: fullname: S Ivanov – volume: 27 start-page: 767 year: 2015 ident: 517_CR15 publication-title: Forum Math. doi: 10.1515/forum-2012-0008 contributor: fullname: Z Muzsnay – volume: 62 start-page: 675 year: 2012 ident: 517_CR14 publication-title: J. Geom. Phys. doi: 10.1016/j.geomphys.2011.04.019 contributor: fullname: VS Matveev – volume: 16 start-page: 2135 year: 2012 ident: 517_CR13 publication-title: Geom. Topol. doi: 10.2140/gt.2012.16.2135 contributor: fullname: VS Matveev – volume: 234 start-page: 1835 year: 1952 ident: 517_CR3 publication-title: C. R. Acad. Sci. Paris contributor: fullname: A Borel – volume: 35 start-page: 25 issue: 1 year: 1981 ident: 517_CR21 publication-title: Tensor contributor: fullname: ZI Szabó – volume: 83 start-page: 279 year: 1955 ident: 517_CR1 publication-title: Bull. Soc. Math. Fr. doi: 10.24033/bsmf.1464 contributor: fullname: M Berger – volume: 73 start-page: 101677 year: 2020 ident: 517_CR6 publication-title: Differ. Geom. Appl. doi: 10.1016/j.difgeo.2020.101677 contributor: fullname: B Hubicska – volume: 14 start-page: 50 year: 2009 ident: 517_CR11 publication-title: I. Szabo. Balkan J. Geom. contributor: fullname: VS Matveev – volume: 74 start-page: 405 year: 2009 ident: 517_CR12 publication-title: Publ. Math. Debr. doi: 10.5486/PMD.2009.4458 contributor: fullname: VS Matveev |
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| Snippet | We show that the set of Finsler metrics on a manifold contains an open everywhere dense subset of Finsler metrics with infinite-dimensional holonomy groups. |
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| SubjectTerms | Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics |
| Title | Almost All Finsler Metrics have Infinite Dimensional Holonomy Group |
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