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

- N. Grosse, Roger Nakad
- Mathematics
- 19 July 2012

We study boundary value problems for the Dirac operator on Riemannian Spin$^c$ manifolds of bounded geometry and with noncompact boundary. This generalizes a part of the theory of boundary value… Expand

Lower Bounds for the Eigenvalues of the Dirac Operator on Spin c Manifolds

- Roger Nakad
- Mathematics
- 28 July 2010

In this paper, we extend the Hijazi inequality, involving the Energy-Momentum tensor, for the eigenvalues of the Dirac operator on Spin c manifolds without boundary. The limiting case is then studied… Expand

Special submanifolds of Spin$^c$ manifolds

- Roger Nakad
- Mathematics
- 9 May 2011

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… Expand

Hypersurfaces of Spinc Manifolds and Lawson Type Correspondence

- Roger Nakad, J. Roth
- Mathematics
- 14 March 2012

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.… Expand

Eigenvalue estimate for the basic Laplacian on manifolds with foliated boundary

- Fida El Chami, Georges Habib, Ola Makhoul, Roger Nakad
- Physics, Mathematics
- 1 November 2018

On a compact Riemannian manifold whose boundary is endowed with a Riemannian flow, we give a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic 1-forms. The equality… Expand

The Energy-Momentum Tensor on Spin Manifolds

- Roger Nakad
- 2020

On Spin 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 manifold. Using the notion of… Expand

The Hijazi inequalities on complete Riemannian Spin c manifolds

- Roger Nakad
- Mathematics
- 23 January 2011

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… Expand

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

- Roger Nakad, J. Roth
- Mathematics
- 12 July 2012

We extend to the eigenvalues of the hypersurface Spin$^c$ Dirac operator well known lower and upper bounds. Examples of limiting cases are then given. Futhermore, we prove a correspondence between… Expand

The twisted Spin c Dirac operator on Kahler submanifolds of the complex projective space

- Georges Habib, Roger Nakad
- Mathematics
- 11 July 2012

Abstract In this paper, we estimate the eigenvalues of the twisted Dirac operator on Kahler submanifolds of the complex projective space C P m and we discuss the sharpness of this estimate for the… Expand

A Hybrid Function Approach to Solving a Class of Fredholm and Volterra Integro-Differential Equations

- Aline Hosry, Roger Nakad, S. Bhalekar
- Mathematics
- 27 May 2020

In this paper, we use a numerical method that involves hybrid and block-pulse functions to approximate solutions of systems of a class of Fredholm and Volterra integro-differential equations. The key… Expand

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