# Hypersurfaces of Spinc Manifolds and Lawson Type Correspondence

@article{Nakad2012HypersurfacesOS,
title={Hypersurfaces of Spinc Manifolds and Lawson Type Correspondence},
journal={Annals of Global Analysis and Geometry},
year={2012},
volume={42},
pages={421-442}
}
• Published 14 March 2012
• Mathematics
• Annals of Global Analysis and Geometry
Simply connected three-dimensional homogeneous manifolds $${\mathbb{E}(\kappa, \tau)}$$, with four-dimensional 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 $${\mathbb{E}(\kappa, \tau)}$$. As application, we get an elementary proof of a Lawson type correspondence for constant mean curvature surfaces in $${\mathbb{E}(\kappa… 19 Citations In this thesis, we aim to make use of Spin^c geometry to study special submanifolds. We start by establishing basic results for the Spin^c Dirac operator. We give then inequalities of Hijazi type • Mathematics International Journal of Mathematics • 2020 Under some dimension restrictions, we prove that totally umbilical hypersurfaces of Spin[Formula: see text] manifolds carrying a parallel, real or imaginary Killing spinor are of constant mean • Mathematics Annals of Global Analysis and Geometry • 2021 The Riemannian product$${\mathbb{M}}_1(c_1) \times {\mathbb{M}}_2(c_2)$$M 1 ( c 1 ) × M 2 ( c 2 ) , where$${\mathbb{M}}_i(c_i) M i ( c i ) denotes the 2-dimensional space form of constant
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• 2014
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