\(\delta\)-homogeneity in Finsler geometry and the positive curvature problem

zbMath1390.53079arXiv1611.00920MaRDI QIDQ1704398

Lei Zhang, Ming Xu

Publication date: 9 March 2018

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.00920

zbMATH Keywords

Finsler spaceflag curvatureFinsler submersion\(\delta \)-homogeneity

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Semisimple Lie groups and their representations (22E46) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60)

Related Items (9)

Standard homogeneous (α1,α2)${\big(\alpha _1,\alpha _2\big)}$‐metrics and geodesic orbit property ⋮ Homogeneous nonlinear splittings and Finsler submersions ⋮ Recent progress on homogeneous Finsler spaces with positive curvature ⋮ The fundamental equations of a pseudo-Finsler submersion ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Geodesic orbit Finsler spaces with \(K \geq 0\) and the (FP) condition ⋮ Homogeneous Finsler spaces and the flag-wise positively curved condition ⋮ Geodesic orbit spheres and constant curvature in Finsler geometry

Cites Work

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• Ricci curvatures of left invariant Finsler metrics on Lie groups
• Classification of generalized normal homogeneous Riemannian manifolds of positive Euler characteristic
• Clifford-Wolf translations of Finsler spaces
• The Chebyshev norm on the Lie algebra of the motion group of a compact homogeneous Finsler manifold
• Homogeneous spaces of curvature bounded below
• Normal homogeneous Finsler spaces
• Homogeneous Finsler spaces and the flag-wise positively curved condition
• Examples of flag-wise positively curved spaces
• Generalized normal homogeneous Riemannian metrics on spheres and projective spaces
• Compact homogeneous Riemannian manifolds with strictly positive curvature
• Isometric submersions of Finsler manifolds
• Homogeneous Finsler Spaces
• The normal homogeneous space (𝖲𝖴(3)×𝖲𝖮(3))/𝖴^{∙}(2) has positive sectional curvature
• On generalized normal homogeneous Randers spaces
• Even dimensional homogeneous Finsler spaces with positive flag curvature
• On \(\delta \)-homogeneous Riemannian manifolds

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