Invariant \((\alpha , \beta)\)-metrics on homogeneous manifolds

DOI10.1007/s00605-007-0529-1zbMath1206.53022OpenAlexW2065936603MaRDI QIDQ1018006

Huihui An, Shaoqiang Deng

Publication date: 13 May 2009

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-007-0529-1

zbMATH Keywords

homogeneous spacesDouglas metricRanders metricBerwald metric\((\alpha, \beta)\) metric

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40)

Related Items (16)

Non-Berwaldian Randers metrics of Douglas type on four-dimensional hypercomplex Lie groups ⋮ Homogeneous Einstein \((\alpha,\beta)\)-metrics on compact simple Lie groups and spheres ⋮ Geodesic vectors of invariant square metrics on nilpotent Lie groups of dimension five ⋮ Invariant vector field on a homogeneous Finsler space with special (α,β)-metric ⋮ Left invariant Randers metrics of Berwald type on tangent Lie groups ⋮ Some Finsler spaces with homogeneous geodesics ⋮ Unnamed Item ⋮ A Short Survey on Lie Theory and Finsler Geometry ⋮ Unnamed Item ⋮ On the Geometry of Some (α, β)-Metrics on the Nilpotent Groups H(p, r) ⋮ On the left invariant Randers and Matsumoto metrics of Berwald type on 3-dimensional Lie groups ⋮ On invariant Matsumoto metrics ⋮ \textbf{S}-curvature and \textbf{E}-curvature of invariant \((\alpha,\beta)\)-metric on homogeneous space ⋮ Naturally reductive homogeneous Finsler spaces ⋮ On the existence of homogeneous geodesics in homogeneous Kropina spaces ⋮ Left invariant lifted $(\alpha,\beta)$-metrics of Douglas type on tangent Lie groups

Cites Work

• The group of isometries of a Finsler space.
• Theory of Finsler spaces with \((\alpha,\beta)\)-metric
• Invariant Randers metrics on homogeneous Riemannian manifolds
• Invariant Finsler metrics on homogeneous manifolds
• Classes of Finsler spaces with \((\alpha,\beta)\)-metrics

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