Niveau: Supérieur, Doctorat, Bac+8
Hypersurfaces of Spinc Manifolds and Lawson Type Correspondence Roger Nakad and Julien Roth March 24, 2012 Abstract Simply connected 3-dimensional homogeneous manifoldsE(?, ?), with 4-dimen- sional isometry group, have a canonical Spinc 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(?, ?). As applica- tion, we get an elementary proof of a Lawson type correspondence for constant mean curvature surfaces in E(?, ?). Real hypersurfaces of the complex projective space and the complex hyperbolic space are also characterized via Spinc spinors. Keywords: Spinc structures, Killing and parallel spinors, isometric immersions, Law- son type correspondence, Sasaki hypersurfaces. Mathematics subject classifications (2010): 58C40, 53C27, 53C40, 53C80. 1 Introduction It is well-known that a conformal immersion of a surface in R3 could be characterized by a spinor field ? satisfying D? = H?, (1) where D is the Dirac operator and H the mean curvature of the surface (see [12] for instance). In [4], Friedrich characterized surfaces in R3 in a geometrically invariant way. More precisely, consider an isometric immersion of a surface (M2, g) into R3.
- killing constant
- dimensional homogeneous
- riemannian surface
- spinor bundle
- constant curvature
- i?
- sider hypersurfaces
- mean curvature
- characterized via spinc spinors