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A brief note on the spectrum of the basic Dirac operator

- Georges Habib, Ken Richardson
- Mathematics
- 14 September 2008

In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation $(M,\mathcal{F})$ with respect to a change of bundle-like metric. We then… Expand

Some remarks on Calabi-Yau and hyper-K\"ahler foliations

- Georges Habib, Luigi Vezzoni
- Mathematics
- 21 June 2013

We study Riemannian foliations whose transverse Levi-Civita connection $\nabla$ has special holonomy. In particular, we focus on the case where $Hol(\nabla)$ is contained either in SU(n) or in Sp(n).… Expand

A new upper bound for the Dirac operator on hypersurfaces

- N. Ginoux, Georges Habib, S. Raulot
- Mathematics
- 5 February 2014

We prove a new upper bound for the first eigenvalue of the Dirac
operator of a compact hypersurface in any Riemannian spin manifold carrying a non-trivial twistor spinor without zeros on the… Expand

Essential norm of Cesàro operators on Lp and Cesàro spaces

- Ihab Al Alam, Loïc Gaillard, Georges Habib, P. Lefèvre, F. Maalouf
- Mathematics
- 15 November 2018

Abstract In this paper, we consider the Cesaro-mean operator Γ acting on some Banach spaces of measurable functions on ( 0 , 1 ) , as well as its discrete version on some sequences spaces. We compute… Expand

NEW COHOMOLOGICAL INVARIANTS OF FOLIATIONS

- Ken Richardson, Georges Habib
- Mathematics
- 2 June 2019

Given a smooth foliation on a closed manifold, basic forms are differential forms that can be expressed locally in terms of the transverse variables. The space of basic forms yields a differential… Expand

Skew Killing spinors in four dimensions

- N. Ginoux, Georges Habib, I. Kath
- Mathematics
- 2 May 2020

This paper is devoted to the classification of 4-dimensional Riemannian spin manifolds carrying skew Killing spinors. A skew Killing spinor ψ is a spinor that satisfies the equation ∇Xψ = AX · ψ with… Expand

Homotopy invariance of cohomology and signature of a Riemannian foliation

- Georges Habib, Ken Richardson
- Mathematics
- 30 March 2017

We prove that any smooth foliation that admits a Riemannian foliation structure has a well-defined basic signature, and this geometrically defined invariant is actually a foliated homotopy invariant.… 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

Geometric aspects of transversal Killing spinors on Riemannian flows

- N. Ginoux, Georges Habib
- Mathematics
- 1 August 2008

We study a Killing spinor type equation on spin Riemannian flows. We prove integrability conditions and partially classify those flows carrying non-trivial solutions.

A spectral estimate for the Dirac operator on Riemannian flows

- N. Ginoux, Georges Habib
- Mathematics
- 2 September 2010

We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on both Sasakian and 3-dimensional… Expand

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