Local study of curvature operators on the hyperbolic space

DOI10.1016/S0021-7824(99)00014-8zbMath0970.53014OpenAlexW2026462545MaRDI QIDQ1305111

Erwann Delay

Publication date: 21 October 2001

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-7824(99)00014-8

zbMATH Keywords

Einstein equationRicci tensorhyperbolic spaceEinstein tensorRiemannian metricsRicci equation

Mathematics Subject Classification ID

Applications of local differential geometry to the sciences (53B50) Local Riemannian geometry (53B20) Methods of local Riemannian geometry (53B21)

Related Items (10)

$L^p$ almost conformal isometries of Sub-Semi-Riemannian metrics and solvability of a Ricci equation ⋮ Resonances for symmetric tensors on asymptotically hyperbolic spaces ⋮ Non-singular space-times with a negative cosmological constant. II: Static solutions of the Einstein-Maxwell equations ⋮ TT-eigentensors for the Lichnerowicz Laplacian on some asymptotically hyperbolic manifolds with warped products metrics ⋮ Inversion of some curvature operators near a parallel Ricci metric ⋮ Inversion d'opérateurs de courbures au voisinage de la métrique euclidienne ⋮ Studies of some curvature operators in a neighborhood of an asymptotically hyperbolic Einstein manifold ⋮ Manifold structures for sets of solutions of the general relativistic constraint equations ⋮ Ricci curvature in the neighborhood of rank-one symmetric spaces. ⋮ Essential spectrum of the Lichnerowicz Laplacian on two tensors on asymptotically hyperbolic manifolds

Cites Work

• Uniqueness and non-existence of metrics with prescribed Ricci curvature
• The Dirichlet problem at infinity for manifolds of negative curvature
• Existence of metrics with prescribed Ricci curvature: Local theory
• Einstein metrics with prescribed conformal infinity on the ball
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Prescription de la courbure de Ricci au voisinage de la métrique hyperbolique
• Analyse précisée d'équations semi-linéaires elliptiques sur l'espace hyperbolique et application à la courbure scalaire conforme
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