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Roger Nakad

Publications and source records attributed to Roger Nakad.

23 records · Page 2Linked to original sources
arXiv2012

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

Simply connected 3-dimensional homogeneous manifolds $E(κ, τ)$, 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 $E(κ, τ)$. As application, we get an elementary proof of a Lawson type correspondence for constant mean curvature surfaces in $E(κ, τ)$. Real hypersurfaces of the complex projective space and the complex hyperbolic space are also characterized via Spin$^c$ spinors.

math.DG↗
arXiv2012

The Energy-Momentum tensor on low dimensional $\Spinc$ manifolds

On a compact surface endowed with any $\Spinc$ structure, we give a formula involving the Energy-Momentum tensor in terms of geometric quantities. A new proof of a Bär-type inequality for the eigenvalues of the Dirac operator is given. The round sphere $\mathbb{S}^2$ with its canonical $\Spinc$ structure satisfies the limiting case. Finally, we give a spinorial characterization of immersed surfaces in $\mathbb{S}^2\times \mathbb{R}$ by solutions of the generalized Killing spinor equation associated with the induced $\Spinc$ structure on $\mathbb{S}^2\times \mathbb{R}$

math.DG↗
arXiv2011

The Hijazi inequalities on complete Riemannian Spin$^c$ manifolds

In this paper, we extend the Hijazi type inequality, involving the Energy-Momentum tensor, to the eigenvalues of the Dirac operator on complete Riemannian Spin$^c$ manifolds without boundary and of finite volume. Under some additional assumptions, using the refined Kato inequality, we prove the Hijazi type inequality for elements of the essential spectrum. The limiting cases are also studied.

math.DG↗
arXiv2010

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 notion of generalized cylinders, we derive the variationnal formula for the Dirac operator under metric deformation and point out that the Energy-Momentum tensor appears naturally as the second fundamental form of an isometric immersion. Finally, we show that generalized $Spin^c$ Killing spinors for Codazzi Energy-Momentum tensor are restrictions of parallel spinors.

math.DG↗