A new upper bound for the Dirac operator on hypersurfaces

by Nicolas Ginoux, Georges Habib and Simon Raulot

Pacific J. Math. 278 (2015), no. 1, 79-101

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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 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.

Nicolas Ginoux, 2/11/2015