22 citations · 65 across the 19 of their papers we have counts for
23 papers
Solving Fredholm integro-differential equations using Hybrid and Block-Pulse functions
Aline Hosry, Roger Nakad, Sachin Bhalekar
In this paper, hybrid and block-pulse functions are used to approximate the solution of a class of Fredholm integro-differential equations that was first studied by Hemeda. By empl…
Hypersurfaces immersed in special Spin manifolds by first eigenspinors
Roger Nakad
Let be a closed orientable hypersurface of dimension , with nonwhere vanishing mean curvature , immersed into a Riemannian Spin manifold carrying a paral…
Totally umbilical hypersurfaces of Spin manifolds carrying special spinor fields
Nadine Große, Roger Nakad
Under some dimension restrictions, we prove that totally umbilical hypersurfaces of Spin manifolds carrying a parallel, real or imaginary Killing spinor are of constant mean cu…
Characterization of hypersurfaces in four dimensional product spaces via two different Spin structures
Roger Nakad, Julien Roth
The Riemannian product , where denotes the -dimensional space form of constant sectional curvature $c_i \in \mathbb…
Hybrid functions approach to solve a class of Fredholm and Volterra integro-differential equations
Aline Hosry, Roger Nakad, Sachin Bhalekar
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…
Rigidity results for Riemannian spin^c manifolds with foliated boundary
Fida Chami, Nicolas Ginoux, Georges Habib +1
Given a Riemannian spin^c manifold whose boundary is endowed with a Riemannian flow, we show that any solution of the basic Dirac equation satisfies an integral inequality dependin…
Spinorially twisted Spin structures, III: CR structures
Rafael Herrera, Roger Nakad, Ivan Tellez
We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifold…
Complex and Lagrangian surfaces of the complex projective plane via Kählerian Killing Spin spinors
Roger Nakad, Julien Roth
The complex projective space of complex dimension has a Spin structure carrying Kählerian Killing spinors. The restriction of one of these Kählerian Killing…
Eigenvalue Estimate for the basic Laplacian on manifolds with foliated boundary, part II
Fida El Chami, George Habib, Ola Makhoul +1
In [4], we gave a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic -forms defined on a compact manifold whose boundary is endowed with a Riemann…
Eigenvalue Estimate for the basic Laplacian on manifolds with foliated boundary
Fida El Chami, Georges Habib, Ola Makhoul +1
In this paper, we give a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic -forms defined on a compact manifold whose boundary is endowed with a…
Eigenvalue Estimates of the Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds
Roger Nakad, Mihaela Pilca
We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact Kähler-Einstein manifold of positive scalar curvature and endowed with particular ${\rm sp…
Rigidity results for spin manifolds with foliated boundary
Fida El Chami, Nicolas Ginoux, Georges Habib +1
In this paper, we consider a compact Riemannian manifold whose boundary is endowed with a Riemannian flow. Under a suitable curvature assumption depending on the O'Neill tensor of…
Complex Generalized Killing Spinors on Riemannian Spin manifolds
Nadine Große, Roger Nakad
In this paper, we extend the study of generalized Killing spinors on Riemannian Spin manifolds started by Moroianu and Herzlich to complex Killing functions. We prove that such…
Riemannian foliations with parallel or harmonic basic forms
Fida EL Chami, Georges Habib, Roger Nakad
In this paper, we consider a Riemannian foliation whose normal bundle carries a parallel or harmonic basic form. We estimate the norm of the O'Neill tensor in terms of the curvatur…
Spinorial Characterization of CR Structures, I
Rafael Hererra, Roger Nakad
We characterize certain CR structures of arbitrary codimension (different from 3, 4 and 5) on Riemannian Spin manifolds by the existence of a Spin structure carrying a stri…
The Spin Dirac Operator on Hypersurfaces and Applications
Roger Nakad, Julien Roth
We extend to the eigenvalues of the hypersurface Spin Dirac operator well known lower and upper bounds. Examples of limiting cases are then given. Futhermore, we prove a corres…
The twisted Spin Dirac operator on Kähler submanifolds of the complex projective space
Georges Habib, Roger Nakad
In this paper, we estimate the eigenvalues of the twisted Dirac operator on Kähler submanifolds of the complex projective space and we discuss the sharpness of this estimat…
Boundary value problems for noncompact boundaries of Spin manifolds and spectral estimates
Nadine Große, Roger Nakad
We study boundary value problems for the Dirac operator on Riemannian Spin manifolds of bounded geometry and with noncompact boundary. This generalizes a part of the theory of…
The Energy-Momentum tensor on low dimensional $\Spinc$ manifolds
Georges Habib, Roger Nakad
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 inequal…
Hypersurfaces of Spin manifolds and Lawson type correspondence
Roger Nakad, Julien Roth
Simply connected 3-dimensional homogeneous manifolds , with 4-dimensional isometry group, have a canonical Spin structure carrying parallel or Killing spinors. The res…
The Hijazi inequalities on complete Riemannian Spin manifolds
Roger Nakad
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 manifolds withou…
The Energy-Momentum tensor on manifolds
Roger Nakad
On 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 ma…
Lower Bounds for the Eigenvalues of the Dirac Operator on Manifolds
Roger Nakad
In this paper, we extend the Hijazi inequality, involving the Energy-Momentum tensor, for the eigenvalues of the Dirac operator on manifolds without boundary. The limiting…