Hypersurfaces of Spin$^c$ manifolds and Lawson type correspondence
Abstract
Simply connected 3-dimensional homogeneous manifolds $E(\kappa, \tau)$, with 4-dimensional isometry group, have a canonical Spin$^c$ structure carrying parallel or Killing spinors. The restriction to any hypersurface of these parallel or Killing spinors allows to characterize isometric immersions of surfaces into $E(\kappa, \tau)$. As application, we get an elementary proof of a Lawson type correspondence for constant mean curvature surfaces in $E(\kappa, \tau)$. Real hypersurfaces of the complex projective space and the complex hyperbolic space are also characterized via Spin$^c$ spinors.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2012
- DOI:
- 10.48550/arXiv.1203.3034
- arXiv:
- arXiv:1203.3034
- Bibcode:
- 2012arXiv1203.3034N
- Keywords:
-
- Mathematics - Differential Geometry;
- 58C40;
- 53C27;
- 53C40;
- 53C80
- E-Print:
- to appear in Annals of Global Analysis and Geometry (AGAG)