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A Singularity Theorem for Twistor Spinors

Florin Alexandru Belgun, Nicolas Ginoux, Hans-Bert Rademacher (2007)

Annales de l’institut Fourier

We study spin structures on orbifolds. In particular, we show that if the singular set has codimension greater than 2, an orbifold is spin if and only if its smooth part is. On compact orbifolds, we show that any non-trivial twistor spinor admits at most one zero which is singular unless the orbifold is conformally equivalent to a round sphere. We show the sharpness of our results through examples.

A spectral estimate for the Dirac operator on Riemannian flows

Nicolas Ginoux, Georges Habib (2010)

Open Mathematics

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 manifolds, and partially classify those satisfying the limiting case. Finally, we compare our estimate with a lower bound in terms of a natural tensor depending on the eigenspinor.

Algebraic analysis of the Rarita-Schwinger system in real dimension three

Alberto Damiano (2006)

Archivum Mathematicum

In this paper we use the explicit description of the Spin– 3 2 Dirac operator in real dimension 3 appeared in (Homma, Y., The Higher Spin Dirac Operators on 3 –Dimensional Manifolds. Tokyo J. Math. 24 (2001), no. 2, 579–596.) to perform the algebraic analysis of the space of nullsolution of the system of equations given by several Rarita–Schwinger operators. We make use of the general theory provided by (Colombo, F., Sabadini, I., Sommen, F., Struppa, D. C., Analysis of Dirac systems and computational...

Clifford and harmonic analysis on cylinders and torii.

Rolf Sören Krausshar, John Ryan (2005)

Revista Matemática Iberoamericana

Cotangent type functions in Rn are used to construct Cauchy kernels and Green kernels on the conformally flat manifolds Rn/Zk where 1 < = k ≤ M. Basic properties of these kernels are discussed including introducing a Cauchy formula, Green's formula, Cauchy transform, Poisson kernel, Szegö kernel and Bergman kernel for certain types of domains. Singular Cauchy integrals are also introduced as are associated Plemelj projection operators. These in turn are used to study Hardy spaces in this...

Do Barbero-Immirzi connections exist in different dimensions and signatures?

L. Fatibene, Mauro Francaviglia, S. Garruto (2012)

Communications in Mathematics

We shall show that no reductive splitting of the spin group exists in dimension 3 ≤ m ≤ 20 other than in dimension m = 4 . In dimension 4 there are reductive splittings in any signature. Euclidean and Lorentzian signatures are reviewed in particular and signature ( 2 , 2 ) is investigated explicitly in detail. Reductive splittings allow to define a global SU ( 2 ) -connection over spacetime which encodes in an weird way the holonomy of the standard spin connection. The standard Barbero-Immirzi (BI) connection used in LQG is...

General theory of Lie derivatives for Lorentz tensors

Lorenzo Fatibene, Mauro Francaviglia (2011)

Communications in Mathematics

We show how the ad hoc prescriptions appearing in 2001 for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier, in a much more general setting encompassing older results of Y. Kosmann about Lie derivatives of spinors.

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