Search results for " Geometry"
showing 10 items of 2294 documents
Automorphisms of $mathbb{A}^{1}$-fibered affine surfaces
2011
We develop technics of birational geometry to study automorphisms of affine surfaces admitting many distinct rational fibrations, with a particular focus on the interactions between automorphisms and these fibrations. In particular, we associate to each surface S of this type a graph encoding equivalence classes of rational fibrations from which it is possible to decide for instance if the automorphism group of S is generated by automorphisms preserving these fibrations.
Curves as measured foliation on noncompact surfaces
1993
In the present work, that regards the Thurston's theory, we prove that, if we choose a closed curve, how we wish, on a noncompact surface, it is always possible to construct a particular masured foliation that has the choosed curve like a leaf; we also prove this foliation has a remarkable property that makes very easy to mesure all homotopy classes of closed curves of our surface. To prove this statement we need some Propositions and some Lemma that we also demonstre.
MULTIRESOLUTION ANALYSIS FOR IRREGULAR MESHES WITH APPEARANCE ATTRIBUTES
2004
We present a new multiresolution analysis framework based on the lifting scheme for irregular meshes with attributes. We introduce a surface prediction opera- tor to compute the detail coefficients for the geometry and the attributes of the model. Attribute analysis gives appearance information to complete the geomet- rical analysis of the model.We present an application to adaptive visualization and some experimental results to show the efficiency of our framework.
Multiresolution Analysis for Meshes with Appearance Attributes
2005
International audience; We present a new multiresolution analysis framework for irregular meshes with attributes based on the lifting scheme. We introduce a surface prediction operator to compute the detail coefficients for the geometry and the attributes of the model. Attribute analysis gives appearance information to complete the geometrical analysis of the model. A set of experimental results are given to show the efficiency of our framework. We present two applications to adaptive visual-ization and denoising.
Semiflexible Polymers in Spherical Confinement: Bipolar Orientational Order Versus Tennis Ball States
2017
Densely packed semiflexible polymers with contour length L confined in spheres with radius R of the same order as L cannot exhibit uniform nematic order. Depending on the chain stiffness (which we vary over a wide range), highly distorted structures form with topological defects on the sphere surface. These structures are completely different from previously observed ones of very long chains winding around the inner surface of spheres and from nematic droplets. At high densities, a thin shell of polymers close to the sphere surface exhibits a tennis ball texture due to the confinement-induced gradual bending of polymer bonds. In contrast, when the contour length of the chains is significant…
Constant angle surfaces in 4-dimensional Minkowski space
2019
Abstract We first define a complex angle between two oriented spacelike planes in 4-dimensional Minkowski space, and then study the constant angle surfaces in that space, i.e. the oriented spacelike surfaces whose tangent planes form a constant complex angle with respect to a fixed spacelike plane. This notion is the natural Lorentzian analogue of the notion of constant angle surfaces in 4-dimensional Euclidean space. We prove that these surfaces have vanishing Gauss and normal curvatures, obtain representation formulas for the constant angle surfaces with regular Gauss maps and construct constant angle surfaces using PDE’s methods. We then describe their invariants of second order and show…
On the range of the attenuated ray transform for unitary connections
2013
We describe the range of the attenuated ray transform of a unitary connection on a simple surface acting on functions and 1-forms. We use this to determine the range of the ray transform acting on symmetric tensor fields.
Surface Studies with Slow Positron Beaks
1984
Slow-positron physics is an exciting and rapidly advancing field. The continuing progress in the development of intense monochromatic beams of low-energy positrons has made it possible to perform a number of landmark experiments, where the interaction of the positron with solid surfaces plays a central role. These experiments either deal with fundamental atomic physics (positronium spectroscopy) or focus on the electronic and atomic properties of the surface region, using positrons as a probe. In the former category, the surface is involved just as an efficient source of positronium-like atoms. On the other hand, in the second category of experiments the surface i s the main object of study…
Subdivisions of Ring Dupin Cyclides Using Bézier Curves with Mass Points
2021
Dupin cyclides are algebraic surfaces introduced for the first time in 1822 by the French mathematician Pierre-Charles Dupin. A Dupin cyclide can be defined as the envelope of a one-parameter family of oriented spheres, in two different ways. R. Martin is the first author who thought to use these surfaces in CAD/CAM and geometric modeling. The Minkowski-Lorentz space is a generalization of the space-time used in Einstein’s theory, equipped of the non-degenerate indefinite quadratic form $$Q_{M} ( \vec{u} ) = x^{2} + y^{2} + z^{2} - c^{2} t^{2}$$ where (x, y, z) are the spacial components of the vector $$ \vec{u}$$ and t is the time component of $$ \vec{u}$$ and c is the constant of the spee…
Humbert surfaces and the Kummer plane
2003
A Humbert surface is a hypersurface of the moduli space A 2 \mathcal A_2 of principally polarized abelian surfaces defined by an equation of the form a z 1 + b z 2 + c z 3 + d ( z 2 2 − z 1 z 3 ) + e = 0 az_1+bz_2+cz_3+d(z_2^2-z_1z_3)+e=0 with integers a , … , e a,\ldots ,e . We give geometric characterizations of such Humbert surfaces in terms of the presence of certain curves on the associated Kummer plane. Intriguingly this shows that a certain plane configuration of lines and curves already carries all information about principally polarized abelian surfaces admitting a symmetric endomorphism with given discriminant.