A Short Survey on Lie Theory and Finsler Geometry

DOI10.1007/978-3-319-62181-4_1zbMath1391.53086OpenAlexW2755698969MaRDI QIDQ4608809

Giovanni Falcone, Ming Xu, Karl Strambach

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_1

zbMATH Keywords

Finsler spaceFinsler manifoldLie theory

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Loops, quasigroups (20N05) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02)

Cites Work

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• Curvatures of homogeneous Randers spaces
• On symmetric Finsler spaces
• Killing vector fields of constant length on locally symmetric Riemannian manifolds
• The \(S\)-curvature of homogeneous Randers spaces
• Invariant \((\alpha , \beta)\)-metrics on homogeneous manifolds
• Homogeneous Einstein-Randers spaces of negative Ricci curvature
• Hopf algebras, renormalization and noncommutative geometry
• Normal homogeneous Finsler spaces
• Homogeneous Finsler spaces and the flag-wise positively curved condition
• Deformation quantization of Poisson manifolds
• The group of isometries of a Finsler space.
• Exact Gerstenhaber algebras and Lie bialgebroids
• On the fundamental equations of homogeneous Finsler spaces
• Left invariant Clifford-Wolf homogeneous \(\alpha, \beta)\)-metrics on compact semisimple Lie groups
• Examples of flag-wise positively curved spaces
• The cohomology structure of an associative ring
• Towards the classification of odd-dimensional homogeneous reversible Finsler spaces with positive flag curvature
• Reversible homogeneous Finsler metrics with positive flag curvature
• Left-symmetric algebras, or pre-Lie algebras in geometry and physics
• Minkowski symmetric Lie algebras and symmetric Berwald spaces
• \((\alpha_1,\alpha_2)\)-metrics and Clifford-Wolf homogeneity
• Clifford-Wolf homogeneous Randers spaces
• Homogeneous Finsler Spaces
• Even dimensional homogeneous Finsler spaces with positive flag curvature
• KILLING FRAMES AND S-CURVATURE OF HOMOGENEOUS FINSLER SPACES
• Domaines bornés homogènes et orbites de groupes de transformations affines

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