Abstract
We give a sharp extrinsic lower bound for the first eigenvaluesof the intrinsic Dirac operator of certain hypersurfaces boundinga compact domain in a spin manifold of negative scalar curvature.Limiting-cases are characterized by the existence, on the domain,of imaginary Killing spinors. Some geometrical applications, as anAlexandrov type theorem, are given.
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Hijazi, O., Montiel, S. & Roldán, A. Dirac Operators on Hypersurfaces of Manifolds with Negative Scalar Curvature. Annals of Global Analysis and Geometry 23, 247–264 (2003). https://doi.org/10.1023/A:1022808916165
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DOI: https://doi.org/10.1023/A:1022808916165