Dirac operators on hypersurfaces of manifolds with negative scalar curvature (Q1810771)

The authors derive a sharp extrinsic lower bound for the first eigenvalues of the intrinsic Dirac operator of certain hypersurfaces which bound a compact domain in a spin manifold of negative scalar curvature. It is shown that the limiting cases are characterized by the existence of imaginary Killing spinors on the domain, and an Alexandrov type theorem is obtained. Contents include: Riemannian spin manifolds and hypersurfaces, bounding hypersurfaces and a Reilly integral inequality, scalar curvature bounded by a negative constant, an eigenvalue boundary value problem, an extrinsic eigenvalue estimate, ambient manifolds with imaginary Killing spinors, hypersurfaces admitting real Killing spinors, and a bibliography containing thirty-four references.