The spinor representation of constant mean curvature one surfaces in the Hyperbolic space

We review and comment on some aspects of the spinor representation for constant mean curvature one surfaces in hyperbolic space developed by Bobenko-Pavlyukevich-Springborn in [1]. The relations with the Bryant representation are addressed and some examples are discusse

The Bianchi-Darboux transform of L-isothermic surfaces

We study an analogue of the classical Bianchi-Darboux transformation for L-isothermic surfaces in Laguerre geometry, the Bianchi-Darboux transformation. We show how to construct the Bianchi-Darboux transforms of an L-isothermic surface by solving an integrable linear differential system. We then establish a permutability theorem for iterated Bianchi-Darboux transforms.Comment: 13 pages, amstex, to be published in IJ

Deformation of Surfaces in Lie Sphere Geometry

The theory of surfaces in Euclidean space can be naturally formulated in the more general context of Legendre surfaces into the space of contact elements. We address the question of deformability of Legendre surfaces with respect to the symmetry group of Lie sphere contact transformations from the point of view of the deformation theory of submanifolds in homogeneous spaces. Necessary and sufficient conditions are provided for a Legendre surface to admit non-trivial deformations, and the corresponding existence problem is discusse

Radiated Immunity Testing of a Device with an External Wire: Repeatibility of Reverberation Chamber Results and Correlation with Anechoic Chamber Results

We present the experimental radiated immunity results of an electronic device with an external wire obtained in reverberation and anechoic chambers. Repeatability and reproducibility of reverberation chamber measurements are investigated by repeating the test in three reverberation chambers with different characteristics. We show how the current state of the art allows a statistical control of RC measurement repeatability within an industrial installation, and that a statistical correlation with AC results frequency by frequency is possible in particular cases relevant to automotive application

Reduction for constrained variational problems on 3D null curves

We consider the optimal control problem for null curves in de Sitter 3-space defined by a functional which is linear in the curvature of the trajectory. We show how techniques based on the method of moving frames and exterior differential systems, coupled with the reduction procedure for systems with a Lie group of symmetries lead to the integration by quadratures of the extremals. Explicit solutions are found in terms of elliptic functions and integrals.Comment: 16 page

Closed trajectories of a particle model on null curves in anti-de Sitter 3-space

We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.Comment: 12 pages, 1 figur

Reduction for the projective arclength functional

We consider the variational problem for curves in real projective plane defined by the projective arclength functional and discuss the integrability of its stationary curves in a geometric setting. We show how methods from the subject of exterior differential systems and the reduction procedure for Hamiltonian systems with symmetries lead to the integration by quadratures of the extrema. A scheme of integration is illustrated

Binary trees, coproducts, and integrable systems

We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.Comment: 15 pages, 6 figures, v2: minor correction in theorem 1, two new appendices adde