Abstract

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

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