Group-invariant solutions for the Ricci curvature equation and the Einstein equation

DOI10.1016/j.jde.2018.08.026zbMath1417.53045OpenAlexW2885570292MaRDI QIDQ2423247

Romildo Pina, João Paulo Dos Santos

Publication date: 21 June 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.08.026

zbMATH Keywords

scalar curvatureRicci tensorconformal metricLie symmetry

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

Noncompact quasi‐Einstein manifolds conformal to a Euclidean space, An analysis of symmetry groups of generalized $m$-quasi-Einstein manifolds, Static Einstein-Maxwell space-time invariant by translation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Metrics with prescribed Ricci curvature on homogeneous spaces
• The Dirichlet problem for the prescribed Ricci curvature equation on cohomogeneity one manifolds
• Uniqueness and non-existence of metrics with prescribed Ricci curvature
• On solutions of the Ricci curvature equation and the Einstein equation
• Symmetry classification of quasi-linear PDE's containing arbitrary functions
• A class of solutions of the Ricci and Einstein equations
• Special conformal groups of a Riemannian manifold and Lie point symmetries of the nonlinear Poisson equation
• Existence of metrics with prescribed Ricci curvature: Local theory
• Prescribing Ricci curvature on open surfaces
• Metrics with prescribed Ricci curvature of constant rank. I: The integrable case
• On metrics satisfying equation \(R_{ij}-\frac{1}{2}Kg_{ij}=T_{ij}\) for constant tensors \(T\)
• On the Ricci and Einstein equations on the pseudo-Euclidean and hyperbolic spaces
• Group classification of the general evolution equation: local and quasilocal symmetries
• Conformal metrics and Ricci tensors in the pseudo-Euclidean space
• Seminar on Differential Geometry. (AM-102)
• The Ricci Curvature Equation with Rotational Symmetry
• Conformal metrics and Ricci tensors on the sphere