The existence of homogeneous geodesics in homogeneous pseudo-Riemannian and affine manifolds

DOI10.1016/j.geomphys.2009.12.015zbMath1190.53010OpenAlexW1997210698WikidataQ115353340 ScholiaQ115353340MaRDI QIDQ967472

Zdeněk Dušek

Publication date: 29 April 2010

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2009.12.015

zbMATH Keywords

Killing vector fieldaffine connectionpseudo-Riemannian manifoldhomogeneous manifoldhomogeneous geodesic

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Geodesics in global differential geometry (53C22) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Linear and affine connections (53B05)

Related Items (24)

Geodesic orbit Riemannian structures on \(\mathbf{R}^n\) ⋮ Four-dimensional pseudo-Riemannian g.o. spaces and manifolds ⋮ On the structure of geodesic orbit Riemannian spaces ⋮ Unnamed Item ⋮ Naturally reductive pseudo-Riemannian spaces ⋮ Geodesics in generalized Wallach spaces ⋮ The minimal number of homogeneous geodesics depending on the signature of the Killing form ⋮ Homogeneous pseudo-Riemannian structures of linear type ⋮ Lorentzian compact manifolds: isometries and geodesics ⋮ Unnamed Item ⋮ Homogeneous geodesics and natural reductivity of homogeneous Gödel-type spacetimes ⋮ Homogeneous geodesics and the critical points of the restricted Finsler function ⋮ Pseudo-Riemannian weakly symmetric manifolds ⋮ On the existence of homogeneous geodesic in homogeneous Finsler spaces ⋮ Geodesic orbit metrics on homogeneous spaces constructed by strongly isotropy irreducible spaces ⋮ The affine approach to homogeneous geodesics in homogeneous Finsler spaces ⋮ Riemannian \(M\)-spaces with homogeneous geodesics ⋮ Constancy of Jacobi osculating rank of g.o. spaces of compact and non-compact type ⋮ Homogeneous geodesics and g.o. manifolds ⋮ Spaces of locally homogeneous affine surfaces ⋮ Unnamed Item ⋮ Homogeneous geodesics of non-reductive homogeneous pseudo-Riemannian 4-manifolds ⋮ The existence of light‐like homogeneous geodesics in homogeneous Lorentzian manifolds ⋮ Totally geodesic hypersurfaces of homogeneous spaces

Cites Work

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• A classification of locally homogeneous connections on 2-dimensional manifolds
• New examples of Riemannian g.o. manifolds in dimension 7
• Homogeneous geodesics in solvable Lie groups
• On six-dimensional pseudo-Riemannian almost g.o. spaces
• Classification of locally homogeneous affine connections with arbitrary torsion on 2-dimensional manifolds
• Penrose limits of homogeneous spaces
• Riemannian flag manifolds with homogeneous geodesics
• Almost g.o. spaces in dimensions 6 and 7
• Geodesic graphs on the 13–dimensional group of Heisenberg type
• Non-reductive Homogeneous Pseudo-Riemannian Manifolds of Dimension Four

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