Totally umbilical hypersurfaces of Spin$^c$ manifolds carrying special spinor fields
Differential Geometry
2019-11-15 v2
Abstract
Under some dimension restrictions, we prove that totally umbilical hypersurfaces of Spin manifolds carrying a parallel, real or imaginary Killing spinor are of constant mean curvature. This extends to the Spin case the result of O. Kowalski stating that, every totally umbilical hypersurface of an Einstein manifold of dimension greater or equal to 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.
Keywords
Cite
@article{arxiv.1910.14302,
title = {Totally umbilical hypersurfaces of Spin$^c$ manifolds carrying special spinor fields},
author = {Nadine Große and Roger Nakad},
journal= {arXiv preprint arXiv:1910.14302},
year = {2019}
}