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A new upper bound for
the Dirac operators on hypersurfaces
Nicolas Ginoux, Georges Habib and Simon Raulot |
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Vol. 278 (2015), No. 1, 79–101
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Abstract |
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We prove a new upper bound for the first eigenvalue of the Dirac operator of a compact hypersurface in any Riemannian spin manifold carrying a nontrivial twistor-spinor without zeros on the hypersurface. The upper bound is expressed as the first eigenvalue of a drifting Schrödinger operator on the hypersurface. Moreover, using a recent approach developed by O. Hijazi and S. Montiel, we completely characterize the equality case when the ambient manifold is the standard hyperbolic space. |
Keywords
global analysis, spectral theory, Dirac operator, geometry
of submanifolds
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Mathematical Subject Classification 2010
Primary: 53C27, 53C40
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Milestones
Received: 19 March 2014
Accepted: 16 January 2015
Published: 30 September 2015
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Authors |
| Nicolas Ginoux | |
| Département informatique IUT de Metz Université de Lorraine Ile du Saulcy CS10628 57045 Metz France |
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| Georges Habib | |
| Faculty of Sciences II Department of Mathematics Lebanese University P.O. Box 90656 Fanar-Matn Lebanon |
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| Simon Raulot | |
| Laboratoire de Mathématiques R.
Salem UMR 6085 CNRS Université de Rouen Avenue de l’Université BP.12 Technopôle du Madrillet 76801 Saint-Étienne-du-Rouvray France |
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