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.

to appear in Annals of Global Analysis and Geometry (AGAG)

References in corpus (2)

• Spinorial Characterization of Surfaces into 3-dimensional homogeneous Manifolds
• Lower Bounds for the Eigenvalues of the Dirac Operator on $Spi{n}^c$ Manifolds

Cited by in corpus (1)

• Spinorial Representation of Submanifolds in Riemannian Space Forms