Extrinsic Killing spinors
By employing certain intrinsic and extrinsic curvature assumptions on a Riemannian spin manifold and its boundary, the authors establish the existence of an isomorphism between the restriction to the boundary of parallel spinors and extrinsic Killing spinors of nonnegative Killing constant. It is shown as a corollary that a complete Ricci-flat spin manifold with mean-convex boundary isometric to a round sphere is necessarily a flat disc. They further suggest that this result may be useful in the Hartle-Hawking `no boundary' proposal in relativistic cosmology. Contents include: an introduction; Riemannian spin manifolds with boundary; parallel spinors and extrinsic Killing spinors; extension of extrinsic Killing spinor fields; and a bibliography of twenty-four items.
scientific article; zbMATH DE number 1965494