Some remarks on the converse of Weyl's conformal theorem

DOI10.1016/j.geomphys.2009.08.002zbMath1183.53065OpenAlexW2094019429MaRDI QIDQ1048993

Graham S. Hall

Publication date: 8 January 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.2009.08.002

zbMATH Keywords

Weyl tensorLorentz metricsRiemannian metricsconformal pseudo-Riemannian metrics

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (10)

The classification of the Weyl conformal tensor in 4-dimensional manifolds of neutral signature ⋮ A study on killing vector fields in four-dimensional spaces ⋮ Universal curvature identities. II. ⋮ Four-dimensional homogeneous manifolds satisfying some Einstein-like conditions ⋮ The geometry of 4-dimensional, Ricci-flat manifolds which admit a metric ⋮ Three-dimensional manifolds with special Cotton tensor ⋮ Conformally Einstein and Bach-flat four-dimensional homogeneous manifolds ⋮ Symmetries in 4-dimensional manifolds with metric of neutral signature ⋮ Homogeneous conformal \(C\)-spaces in dimension four ⋮ Some comparisons of the Weyl conformal tensor and its classification in 4-dimensional Lorentz, neutral or positive definite signatures

Cites Work

• Curvature collineations and the determination of the metric from the curvature in General Relativity
• Algebraic determination of the metric from the curvature in general relativity
• Some remarks on the symmetries of the curvature and Weyl tensors
• Exact Solutions of Einstein's Field Equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Some remarks on the converse of Weyl's conformal theorem