We study the existence of natural and projectively equivariant quantizations for differential operators acting between order 1 vector bundles over a smooth manifold M . To that aim, we make use of the Thomas-Whitehead approach of projective structures and construct a Casimir operator depending on a projective Cartan connection. We attach a scalar parameter to every space of differential operato...

Let $\mathcal C$ be a class of Hausdorff topological semigroups which contains all zero-dimensional semigroups. A semigroup $X$ is called C$-$closed$ if closed in each $Y\in \mathcal containing as discrete subsemigroup; $projectively$ for congruence $\approx$ on the quotient $X/_\approx$ C$-closed. $chain$-$finite$ any infinite set $I\subseteq X$ there are elements $x,y\in I$ such that $xy\noti...

Projectively invariant shape descriptors allow fast indexing into model libraries without the need for pose computation or camera calibration. This paper describes progress in building a model based vision system for plane objects that uses algebraic projective invari-ants. We give a brief account of these descriptors and then describe the recognition system, giving examples of the invariant te...

In this note, we prove that for any finite dimensional vector space V over C, and for a finite cyclic group G, the projective variety P(V)/G is projectively normal with respect to the descent of O(1) ⊗|G| by a method using toric variety, and deduce the EGZ theorem as a consequence.

for arbitrary vector fieldsX, Y , Z, U , V ∈ χ(Mn), whereD denotes the operator of covariant differentiation with respect to the Riemannian metric g and A, B, C, D and E are 1−forms (not simultaneously zero). The 1−forms are called the associated 1−forms of the manifold and an n−dimensional manifold of this kind is denoted by (WS)n. Tamassy and Binh [14] further studied weakly symmetric Sasakia...

A number of studies have resulted in the finding of a 3-D perceptual anisotropy, whereby spatial intervals oriented in depth are perceived to be smaller than physically equal intervals in the frontoparallel plane. In this experiment, we examined whether this anisotropy is scale invariant. The stimuli were L shapes created by two rods placed flat on a level grassy field, with one rod defining a ...

We discuss how gerbes may be used to set up a consistent Lagrangian approach to the WZW models with boundary. The approach permits to study in detail possible boundary conditions that restrict the values of the fields on the worldsheet boundary to brane submanifolds in the target group. Such submanifolds are equipped with an additional geometric structure that is summarized in the notion of a g...