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- Title
Totally umbilical hypersurfaces of Spinc manifolds carrying special spinor fields.
- Authors
Große, Nadine; Nakad, Roger
- Abstract
Under some dimension restrictions, we prove that totally umbilical hypersurfaces of Spin c manifolds carrying a parallel, real or imaginary Killing spinor are of constant mean curvature. This extends to the Spin c case the result of 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.
- Subjects
HYPERSURFACES; EINSTEIN manifolds; RIEMANNIAN manifolds; DIFFERENTIAL forms; CURVATURE; SUBMANIFOLDS; SASAKIAN manifolds; DIMENSION theory (Algebra)
- Publication
International Journal of Mathematics, 2020, Vol 31, Issue 12, pN.PAG
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X20501001