70 citations · 395 across the 55 of their papers we have counts for
12 papers · 1 filter
Lagrangian configurations and symplectic cross-ratios
Charles Conley, Valentin Ovsienko
We consider moduli spaces of cyclic configurations of lines in a -dimensional symplectic vector space, such that every set of consecutive lines generates a Lagrangian s…
Riemannian Curl in Contact Geometry
Sofiane Bouarroudj, Valentin Ovsienko
We consider a contact manifold with a pseudo-Riemannian metric and define a contact vector field intrinsically associated to this pair of structures. We call this new differential…
Higher Trace and Berezinian of Matrices over a Clifford Algebra
Tiffany Covolo, Valentin Ovsienko, Norbert Poncin
We define the notions of trace, determinant and, more generally, Berezinian of matrices over a (Z_2)^n graded commutative associative algebra. The applications include a new approa…
Hyperbolic Carathéodory conjecture
Valentin Ovsienko, Serge Tabachnikov
A quadratic point on a surface in is a point at which the surface can be approximated by a quadric abnormally well (up to order 3). We conjecture that the least number of qu…
Vector fields in the presence of a contact structure
Valentin Ovsienko
We consider the Lie algebra of all vector fields on a contact manifold as a module over the Lie subalgebra of contact vector fields. This module is split into a direct sum of two s…
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…
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.
Projectively equivariant symbol calculus
P. B. A. Lecomte, V. Yu. Ovsienko
The spaces of linear differential operators on acting on tensor densities of degree and the space of functions on which are polynomial on t…
Conformally equivariant quantization
C. Duval, V. Ovsienko
Let be a pseudo-Riemannian manifold and the space of densities of degree on . We study the space of second-order differential operators from…