Existence of metrics with prescribed Ricci curvature: Local theory

DOI10.1007/BF01389010zbMath0489.53014MaRDI QIDQ1166783

Dennis M. DeTurck

Publication date: 1981

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142846

zbMATH Keywords

integrability conditionRicci tensorNash-Moser implicit function theoremanalytic metricscontracted second Bianchi identity

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Analyticity in context of PDEs (35A20) Local Riemannian geometry (53B20) Implicit function theorems; global Newton methods on manifolds (58C15)

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Cites Work

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• The imbedding problem for Riemannian manifolds
• Elliptic operators and compact groups
• Existence theorems for analytic linear partial differential equations
• Integrability criteria for systems of nonlinear partial differential equations
• Some decompositions of the space of symmetric tensors on a Riemannian manifolds
• A NEW TECHNIQUE FOR THE CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS
• Comparison theorems for compact symmetric spaces
• The equation of prescribed Ricci curvature
• Shorter Notes: Another Proof of Bianchi's Identity in Riemannian Geometry
• Some regularity theorems in riemannian geometry
• Quelques formules de variation pour une structure riemannienne
• An algebraic model of transitive differential geometry

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