Holonomy Theory of Finsler Manifolds

DOI10.1007/978-3-319-62181-4_12zbMath1392.53079OpenAlexW2755834475MaRDI QIDQ4608821

Zoltán Muzsnay, Péter T. Nagy

Publication date: 28 March 2018

Published in: Lie Groups, Differential Equations, and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-62181-4_12

zbMATH Keywords

curvatureholonomy groupFinsler manifoldholonomy algebraparallel translationFinsler surfacestangent algebrasinfinitesimal holonomy algebraBryant-Shen 2-spherescurvature algebraFinsler holonomyinfinite-dimensional curvature algebraprojectively flat Finsler manifoldspary manifoldthe Berwald translate

Mathematics Subject Classification ID

Issues of holonomy in differential geometry (53C29) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60)

Related Items (1)

Rigidity of Busemann convex Finsler metrics

Cites Work

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• Finsler 2-manifolds with maximal holonomy group of infinite dimension
• Projectively flat Finsler 2-spheres of constant curvature
• Two-dimensional Finsler metrics with constant flag curvature
• Projectively flat Randers metrics with constant flag curvature
• Projectively flat Finsler manifolds with infinite dimensional holonomy
• Sur le groupe des difféomorphismes du tore
• Differentiable fibre spaces and mappings compatible with Riemannian metrics
• Tangent Lie algebras to the holonomy group of a Finsler manifold
• Holonomy of a class of bundles with fibre metrics
• Projectively flat Finsler metrics of constant flag curvature
• Characterization of projective Finsler manifolds of constant curvature having infinite dimensional holonomy group
• ON A CLASS OF PROJECTIVELY FLAT FINSLER METRICS WITH CONSTANT FLAG CURVATURE
• Finsler manifolds with non-Riemannian holonomy
• Nichtlineare Zusammenhänge und deren Holonomiegruppen.
• Regularity of infinite-dimensional Lie groups by metric space methods

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