Self-dual Kähler manifolds and Einstein manifolds of dimension four
Andrzej Derdziński (1983)
Compositio Mathematica
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Displaying similar documents to “Kähler manifolds with small eigenvalues of the Dirac operator and a conjecture of Lichnerowicz”
Self-dual Kähler manifolds and Einstein manifolds of dimension four
Lorentzian manifolds with special holonomy and parallel spinors
Leistner, Thomas
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The author studies the holonomy group of a simply connected indecomposable and reducible Lorentzian spin manifold under the condition that they admit parallel spinors. He shows that there are only two possible situations: either the manifold is a so-called Brinkmann wave or it has Abelian holonomy and is a pp-manifold – a generalization of a plane-wave. The author gives also sufficient conditions for a Brinkmann wave to have as holonomy the semidirect product of holonomy group of a Riemannian...
Compact Kähler manifolds with hermitian semipositive anticanonical bundle
Jean-Pierre Demailly, Thomas Peternell, Michael Schneider (1996)
Compositio Mathematica
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Compact Six-Dimensional Kähler Spin Manifolds of Positive Scalar Curvature with the Smallest Possible First Eigenvalue of the Dirac Operator.
K.-D. Kirchberg (1988)
Mathematische Annalen
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Einstein manifolds, volume rigidity and Seiberg-Witten theory
Andrea Sambusetti (1998-1999)
Séminaire de théorie spectrale et géométrie
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Einstein manifolds of positive scalar curvature with arbitrary second Betti number.
Boyer, Charles P., Galicki, Krzysztof, Mann, Benjamin M., Rees, Elmer G. (1996)
Balkan Journal of Geometry and its Applications (BJGA)
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A spectral estimate for the Dirac operator on Riemannian flows
Nicolas Ginoux, Georges Habib (2010)
Open Mathematics
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We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on both Sasakian and 3-dimensional manifolds, and partially classify those satisfying the limiting case. Finally, we compare our estimate with a lower bound in terms of a natural tensor depending on the eigenspinor.