9 papers
Conformally invariant differential operators on tensor densities
V. Ovsienko, P. Redou
Let be the space of tensor densities on of degree (or, equivalently, of conformal densities of degree ) considered as a module over the Lie algebr…
Methods of Equivariant Quantization
C. Duval, P. Lecomte, V. Ovsienko
This article is a survey of recent work of the authors developing a new approach to quantization based on the equivariance with respect to some Lie group of symmetries. Examples ar…
Projective geometry of polygons and discrete 4-vertex and 6-vertex theorems
V. Ovsienko, S. Tabachnikov
The paper concerns discrete versions of the three well-known results of projective differential geometry: the four vertex theorem, the six affine vertex theorem and the Ghys theore…
Conformally equivariant quantization: Existence and uniqueness
C. Duval, P. Lecomte, V. Ovsienko
We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-Riemannian manifold $(M,\rg)$. In other words…
Deforming the Lie algebra of vector fields on inside the Lie algebra of pseudodifferential symbols on
C. Roger, V. Ovsienko
We classify nontrivial deformations of the standard embedding of the Lie algebra $\Vect(S^1)$ of smooth vector fields on the circle, into the Lie algebra~$\PD(S^1)$ of pseudodiffer…
Lorentzian worldlines and Schwarzian derivative
C. Duval, V. Ovsienko
We relate in this note the classical Schwarzian derivative to the curvature of time-like curves in Lorentz surfaces of constant curvature.