Curvature invariants, Killing vector fields, connections and cohomogeneity

DOI10.1090/S0002-9939-08-09669-XzbMath1161.53034arXiv0801.3211OpenAlexW1978354780MaRDI QIDQ3617597

Carlos E. Olmos, Sergio Console

Publication date: 30 March 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.3211

zbMATH Keywords

curvature invariantsKilling vector fieldsWeyl invariantshomogeneous Riemannian manifoldscohomogeneity

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (10)

Homogeneous Riemannian manifolds with non-trivial nullity ⋮ The index of symmetry of three-dimensional Lie groups with a left-invariant metric ⋮ Isometry groups of three-dimensional Lie groups ⋮ Infinitesimal isometries along curves and generalized Jacobi equations ⋮ Differential invariants and symmetry: Riemannian metrics and beyond ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ Counting the number of Killing vectors in a 3D spacetime ⋮ Differential invariants of Kundt spacetimes ⋮ On the extendability of parallel sections of linear connections ⋮ A criterion for the existence of Killing vectors in 3D

Cites Work

• On two theorems of I. M. Singer about homogeneous spaces
• Natural tensors on Riemannian manifolds
• Holonomy and the Lie Algebra of Infinitesimal Motions of a Riemannian Manifold
• Curvature invariants, differential operators and local homogeneity
• Curvature invariants in type- N spacetimes
• Penrose limits, supergravity and brane dynamics
• A metric with no symmetries or invariants
• Level sets of scalar Weyl invariants and cohomogeneity
• On spacetimes with constant scalar invariants
• Infinitesimally homogeneous spaces

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