Totally umbilical hypersurfaces of Spinc manifolds carrying special spinor fields
Abstract
Under some dimension restrictions, we prove that totally umbilical hypersurfaces of Spinc manifolds carrying a parallel, real or imaginary Killing spinor are of constant mean curvature. This extends to the Spinc case the result of O. Kowalski stating that, every totally umbilical hypersurface of an Einstein manifold of dimension greater or equal to 3 is of constant mean curvature. As an application, we prove that there are no extrinsic hypersheres in complete Riemannian Spin manifolds of non-constant sectional curvature carrying a parallel, Killing or imaginary Killing spinor.
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