A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors

DOI10.1007/BF01210797zbMath0593.58040MaRDI QIDQ1076393

Oussama Hijazi

Publication date: 1986

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Dirac operatorEinstein manifoldconformal structureYamabe operatorRicci-flat manifoldcompact Riemannian spin manifold

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global Riemannian geometry, including pinching (53C20) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60)

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Cites Work

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• Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
• On the structure of manifolds with positive scalar curvature
• Spin and scalar curvature in the presence of a fundamental group. I
• The classification of simply connected manifolds of positive scalar curvature
• Scalar curvature and conformal deformation of Riemannian structure
• Harmonic spinors
• Clifford modules
• Der erste Eigenwert des Dirac‐Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung
• A remark on the first eigenvalue of the Dirac operator on 4-dimensional manifolds
• Compact four-dimensional Einstein manifolds

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