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arXiv · 1402.1049

A new upper bound for the Dirac operator on hypersurfaces

Nicolas Ginoux·Georges Habib·Simon Raulot
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Abstract

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 Schr\"odinger 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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Nicolas Ginoux, Georges Habib, Simon Raulot. 2014-02-05. A new upper bound for the Dirac operator on hypersurfaces. https://doi.org/10.2140/pjm.2015.278.79

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