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A new upper bound for the Dirac operator on hypersurfaces

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Ginoux, Nicolas ; Habib, Georges ; Raulot, Simon
Date of publication of this fulltext: 08 Apr 2014 08:44


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 non-trivial 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.

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