Conformal metrics and Ricci tensors in the pseudo-Euclidean space

DOI10.1090/S0002-9939-00-05817-2zbMath0978.53080OpenAlexW2137896294MaRDI QIDQ2701594

Keti Tenenblat, Romildo Pina

Publication date: 19 February 2001

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-00-05817-2

zbMATH Keywords

conformal metricspseudo-Euclidean spaceprescribed Ricci tensor

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (7)

On solutions of the Ricci curvature equation and the Einstein equation ⋮ A class of solutions of the Ricci and Einstein equations ⋮ Prescribed diagonal Schouten tensor in locally conformally flat manifolds ⋮ Group-invariant solutions for the Ricci curvature equation and the Einstein equation ⋮ On the Ricci and Einstein equations on the pseudo-Euclidean and hyperbolic spaces ⋮ Prescribed Schouten tensor in locally conformally flat manifolds ⋮ On metrics satisfying equation \(R_{ij}-\frac{1}{2}Kg_{ij}=T_{ij}\) for constant tensors \(T\)

Cites Work

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• Uniqueness and non-existence of metrics with prescribed Ricci curvature
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• On conformal scalar curvature equations in \({\mathbb{R}}^ n\)
• Existence of metrics with prescribed Ricci curvature: Local theory
• Prescribing Ricci curvature on open surfaces
• On metrics satisfying equation \(R_{ij}-\frac{1}{2}Kg_{ij}=T_{ij}\) for constant tensors \(T\)
• The scalar curvature equation on \(\mathbb{R}^ n\) and \(S^ n\)
• On solutions of δu=f(u)
• Prescribing a Ricci Tensor in a Conformal Class of Riemannian Metrics
• The Ricci Curvature Equation with Rotational Symmetry
• Conformal Diffeomorphisms Preserving the Ricci Tensor

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