The first eigenvalue of the Dirac operator on compact Kähler manifolds

DOI10.1007/BF02099477zbMath0832.53054MaRDI QIDQ1894864

Andrei Moroianu

Publication date: 22 August 1995

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

zbMATH Keywords

Dirac operatorfirst eigenvalueKähler spin manifold

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Spectral problems; spectral geometry; scattering theory on manifolds (58J50)

Related Items (16)

A characterization of Dirac morphisms ⋮ Eigenforms of the spin Laplacian and projectable spinors for principal bundles ⋮ On a characteristic of the first eigenvalue of the Dirac operator on compact spin symmetric spaces with a Kähler or quaternion-Kähler structure ⋮ The Dirac operator on generalized Taub-NUT spaces ⋮ Imaginary Kählerian Killing spinors I ⋮ The spectrum of the twisted Dirac operator on Kähler submanifolds of the complex projective space ⋮ Energy-momentum tensor on foliations ⋮ Generalized Killing spinors on Einstein manifolds ⋮ Kählerian twistor spinors ⋮ Dirac operators on Lagrangian submanifolds ⋮ Eigenvalue estimates for the Dirac operator on Kähler-Einstein manifolds of even complex dimension ⋮ Vafa-Witten bound on the complex projective space ⋮ Spin\(^{c}\) geometry of Kähler manifolds and the Hodge Laplacian on minimal Lagrangian sub\-manifolds ⋮ The first eigenvalue of the Kohn-Dirac operator on CR manifolds ⋮ Kähler manifolds with small eigenvalues of the Dirac operator and a conjecture of Lichnerowicz ⋮ Unnamed Item

Cites Work

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• On compact Kähler manifolds with positive definite Ricci tensor
• Compact six-dimensional Kähler spin manifolds of positive scalar curvature with the smallest possible first eigenvalue of the Dirac operator
• An estimation for the first eigenvalue of the Dirac operator on closed Kähler manifolds of positive scalar curvature
• Quaternionic Kaehler manifolds
• Eigenvalues of the Dirac operator on compact Kähler manifolds
• Quaternionic reduction and Einstein manifolds
• Real Killing spinors and holonomy
• The fundamental equations of a submersion
• On the differential geometry of foliations
• Der erste Eigenwert des Dirac‐Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung
• Characteristic Classes. (AM-76)

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