Hypersurfaces of Spinc Manifolds and Lawson Type Correspondence

@article{Nakad2012HypersurfacesOS,
  title={Hypersurfaces of Spinc Manifolds and Lawson Type Correspondence},
  author={Roger Nakad and Julien Roth},
  journal={Annals of Global Analysis and Geometry},
  year={2012},
  volume={42},
  pages={421-442}
}
  • Roger NakadJ. Roth
  • 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… 

Special submanifolds of Spin$^c$ manifolds

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

Totally umbilical hypersurfaces of Spinc manifolds carrying special spinor fields

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

Characterization of hypersurfaces in four-dimensional product spaces via two different Spinc structures

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

Eigenvalue Estimates of the spin c Dirac Operator and Harmonic Forms on Kahler{Einstein Manifolds

We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact Kahler{Einstein manifold of positive scalar curvature and endowed with particular spin c structures. The

Spinorial Characterization of CR Structures, I

We characterize certain CR structures of arbitrary codimension (different from 3, 4 and 5) on Riemannian Spin$^c$ manifolds by the existence of a Spin$^c$ structure carrying a strictly partially pure

Spinorial Representation of Submanifolds in Riemannian Space Forms

In this paper we give a spinorial representation of submanifolds of any dimension and codimension into Riemannian space forms in terms of the existence of so called generalized Killing spinors. We

Boundary value problems for noncompact boundaries of Spinc manifolds and spectral estimates

We study boundary value problems for the Dirac operator on Riemannian Spinc manifolds of bounded geometry and with noncompact boundary. This generalizes a part of the theory of boundary value

Complex Generalized Killing Spinors on Riemannian Spinc Manifolds

In this paper, we extend the study of generalized Killing spinors on Riemannian Spinc manifolds started by Moroianu and Herzlich to complex Killing functions. We prove that such spinor fields are

References

SHOWING 1-10 OF 31 REFERENCES

The Spin$^c$ Dirac Operator on Hypersurfaces and Applications

Spinc geometry of Kähler manifolds and the Hodge Laplacian on minimal Lagrangian submanifolds

From the existence of parallel spinor fields on Calabi-Yau, hyper-Kähler or complex flat manifolds, we deduce the existence of harmonic differential forms of different degrees on their minimal

The Spinor Representation of Surfaces in Space

The spinor representation is developed for conformal immersions of Riemann surfaces into space. We adapt the approach of Dennis Sullivan, which treats a spin structure on a Riemann surface M as a

Isometric immersions into 3-dimensional homogeneous manifolds

We give a necessary and sufficient condition for a 2-dimensional Riemannian manifold to be locally isometrically immersed into a 3-dimensional homogeneous Riemannian manifold with a 4-dimensional

Generalized Killing Spinors and Conformal Eigenvalue Estimates for Spinc Manifolds

In this paper we prove the Spinc analog of the Hijazi inequality on the first eigenvalue of the Dirac operator on compact Riemannian manifolds and study its equality case. During this study, we are

The Energy-Momentum tensor on $Spin^c$ manifolds

On $Spin^c$ manifolds, we study the Energy-Momentum tensor associated with a spinor field. First, we give a spinorial Gauss type formula for oriented hypersurfaces of a $Spin^c$ manifold. Using the

On the Spinor Representation of Surfaces in Euclidean 3-Space. ∗

Spinc Manifolds and Complex Contact Structures

Abstract:In this paper we extend our notion of projectable spinors ([9], Ch.1) to the framework of Spinc manifolds and deduce the basic formulas relating spinors on the base and the total space of