Lower bounds for the first eigenvalue of the Dirac operator on compact Riemannian manifolds

DOI10.1016/j.difgeo.2011.02.004zbMath1222.53052OpenAlexW1985994900WikidataQ115356972 ScholiaQ115356972MaRDI QIDQ546126

Klaus-Dieter Kirchberg

Publication date: 24 June 2011

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2011.02.004

zbMATH Keywords

Riemannian manifoldDirac operatorlower boundfirst eigenvalue

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Spin and Spin({}^c) geometry (53C27)

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Cites Work

• The first eigenvalue of the Dirac operator on locally reducible Riemannian manifolds
• The Dirac spectrum
• A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors
• An estimation for the first eigenvalue of the Dirac operator on closed Kähler manifolds of positive scalar curvature
• Eigenvalue estimates for the Dirac operator on quaternionic Kähler manifolds
• An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold admitting parallel one-form
• Eigenvalue estimates for the Dirac operator depending on the Weyl tensor
• Curvature dependent lower bounds for the first eigenvalue of the Dirac operator
• Eigenvalue estimates of the Dirac operator depending on the Ricci tensor
• Real Killing spinors and holonomy
• Der erste Eigenwert des Dirac‐Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung