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.

中文翻译：

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带有特殊旋量场的 Spinc 流形的全脐超曲面

在某些维度限制下，我们证明了带有平行、实数或虚数 Killing 旋量的 Spin[公式：见正文] 流形的完全脐超曲面具有恒定的平均曲率。这延伸到自旋[公式：见文本]的情况，科瓦尔斯基的结果指出，尺寸大于或等于[公式：见文本]的爱因斯坦流形的每个完全脐超曲面都具有恒定的平均曲率。作为一个应用，我们证明在带有平行、Killing 或虚构的 Killing 旋量的非恒定截面曲率的完全黎曼 [公式：见文本] 流形中不存在外在超球面。