Uniqueness and non-existence of metrics with prescribed Ricci curvature

DOI10.1016/S0294-1449(16)30417-6zbMath0556.53026OpenAlexW117985041WikidataQ125913823 ScholiaQ125913823MaRDI QIDQ760921

Dennis M. DeTurck, Norihito Koiso

Publication date: 1984

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_1984__1_5_351_0

zbMATH Keywords

Ricci tensorLevi-Civita connection

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Local Riemannian geometry (53B20)

Related Items (22)

Prescribing Ricci curvature on homogeneous spaces ⋮ On solutions of the Ricci curvature equation and the Einstein equation ⋮ $L^p$ almost conformal isometries of Sub-Semi-Riemannian metrics and solvability of a Ricci equation ⋮ Prescribed diagonal Schouten tensor in locally conformally flat manifolds ⋮ Vanishing theorems for harmonic mappings into non-negatively curved manifolds and their applications ⋮ Metrics with prescribed Ricci curvature near the boundary of a manifold ⋮ Prescribed diagonal Ricci tensor in locally conformally flat manifolds ⋮ Inversion of some curvature operators near a parallel Ricci metric ⋮ Counting holomorphic connections with a prescribed Ricci tensor ⋮ Group-invariant solutions for the Ricci curvature equation and the Einstein equation ⋮ Conformal metrics and Ricci tensors in the pseudo-Euclidean space ⋮ Ricci iteration on homogeneous spaces ⋮ The Cauchy-Kowalevski theorem applied for counting connections with a prescribed Ricci tensor ⋮ Inversion d'opérateurs de courbures au voisinage de la métrique euclidienne ⋮ The prescribed Ricci curvature problem for naturally reductive metrics on compact Lie groups ⋮ Harmonic transforms of complete Riemannian manifolds ⋮ Prescribing a Ricci Tensor in a Conformal Class of Riemannian Metrics ⋮ On the Ricci and Einstein equations on the pseudo-Euclidean and hyperbolic spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Local study of curvature operators on the hyperbolic space ⋮ Prescribing Ricci curvature on a product of spheres

Cites Work

• Curvatures of left invariant metrics on Lie groups
• Métriques kählériennes et fibrés holomorphes
• Curvature operators: pinching estimates and geometric examples
• A Report on Harmonic Maps
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