Hypersurfaces of Spin$^c$ manifolds and Lawson type correspondence

Roger Nakad; Julien Roth

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arXiv · 1203.3034

Hypersurfaces of Spin$^c$ manifolds and Lawson type correspondence

Roger Nakad·Julien Roth

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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.

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Roger Nakad, Julien Roth. 2012-03-14. Hypersurfaces of Spin$^c$ manifolds and Lawson type correspondence. https://arxiv.org/abs/1203.3034

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