Imaginary Kählerian Killing spinors I

We describe and to some extent characterize a new family of Kähler spin manifolds admitting non-trivial imaginary Kählerian Killing spinors.     

Geometric aspects of transversal Killing spinors on Riemannian flows

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

Une nouvelle estimation extrinsèque du spectre de l'opérateur de Dirac

We prove a new upper bound for the smallest eigenvalues of the Dirac operator on a compact hypersurface of the hyperbolic space. To cite this article: N. Ginoux, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Skew Killing spinors in four dimensions

Annals of Global Analysis and Geometry - This paper is devoted to the classification of 4-dimensional Riemannian spin manifolds carrying skew Killing spinors. A skew Killing spinor $$\psi $$ is a...     

Sur la détermination du périmètre de l'ovale à huit centres

This note aims to present the history of the main researches carried out to represent an ellipse by means of an eight-centered oval and to complete them by giving a geometrical demonstration of the formulas expressing the coordinates of the centers, the radii and the central angles of these arcs of circles making up this oval. These formulas will make it possible to determine its perimeter and thus to approximate the value of that of the ellipse. This result could be useful for archaeologists, who will test the hypothesis according to which some Roman amphitheatres, such as the Coliseum, were built from eight-centered ovals.     

A spectral estimate for the Dirac operator on Riemannian flows

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.     

Heat of adsorption of carbon dioxyde and ethene on zeolites a exchanged with Li+, Ni2+ and Cu2+

Various contents of Li⁺, Ni²⁺ or Cu²⁺ were introduced in zeolite NaA by conventional cation exchange. Crystal damages are observed on samples having suffered the lowerpH. The heat of adsorption of CO₂ and C₂H₄ was determined by isothermal calorimetry. Very high initial heats (100–120 kJ mol^?1) are found in NaA as well as in Li⁺ exchanged samples, perhaps due to chemisorption on alkaline cations; they vanish when Ni²⁺ or Cu²⁺ replaces more than 20% of Na⁺, in like manner with Co²⁺ or ZnI²⁺. For the adsorption of C₂H₄, high initial heats are absent in the case of NaA, but gradually appear when divalent cations are introduced. Apart from these strong initial values, the heats of adsorption present a plateauvs. the adsorbed amount. Abnormal low values at the plateau are indicative of crystal damages.     

On the destabilization of a periodically driven three-dimensional torus

We report experimental evidence of the destabilization of a 3D torus obtained when a small subharmonic perturbation is added to a 2D torus characteristic of a driven relaxation oscillator. The Poincaré sections indicate that the torus breakup is sensitive to the phase difference between the main driving frequency and its first subharmonic perturbing component. The observed transition confirms the Newhouse, Ruelle and Takens quasiperiodic transition to chaos on a 3D torus. Numerical results on a sinusoidally perturbed circle map mirror the experimental results and confirm the key role of the phase difference in the transition between distinct dynamical regimes.

     

The spectrum of the Dirac operator on SU<Subscript>2</Subscript>/Q<Subscript>8</Subscript>

We compute the fundamental Dirac operator for the three-parameter-family of homogeneous Riemannian metrics and the four different spin structures on SU₂/Q₈, where Q₈ denotes the group of quaternions. We deduce its spectrum for the Berger metrics and show the sharpness of Christian Bär’s upper bound for the smallest Dirac eigenvalue in the particular case where SU₂/Q₈ is a homogeneous minimal hypersurface of S ⁴.