Results 11  20
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62
Generalized Wilczynski invariants for nonlinear ordinary differential equations
, 2007
"... Abstract. We show that classical Wilczynski–Seashi invariants of linear systems of ordinary differential equations are generalized in a natural way to contact invariants of nonlinear ODEs. We explore geometric structures associated with equations that have vanishing generalized Wilczynski invarian ..."
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Cited by 8 (2 self)
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Abstract. We show that classical Wilczynski–Seashi invariants of linear systems of ordinary differential equations are generalized in a natural way to contact invariants of nonlinear ODEs. We explore geometric structures associated with equations that have vanishing generalized Wilczynski invariants and establish relationship of such equations with deformation theory of rational curves on complex algebraic surfaces. 1.
Multidimensional Schwarzian derivative revisited
, 2001
"... We give intrinsic formula for the multidimensional Schwarzian derivative on a manifold M endowed with a projective connection. This Schwarzian derivative is naturally related to the space of secondorder linear differential operators acting on tensor densities on M. 1 ..."
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Cited by 6 (6 self)
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We give intrinsic formula for the multidimensional Schwarzian derivative on a manifold M endowed with a projective connection. This Schwarzian derivative is naturally related to the space of secondorder linear differential operators acting on tensor densities on M. 1
Schwarzian derivative related to modules of differential operators on a locally projective manifold
, 1998
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Cohomology of the vector fields Lie algebras on RP 1 acting on bilinear differential operators
 Int. Jour. Geom. Methods. Mod. Phys
"... The main topic of this paper is two folds. First, we compute the first relative cohomology group of the Lie algebra of smooth vector fields on the projective line, Vect(RP 1), with coefficients in the space of bilinear differential operators that act on tensor densities, Dλ,ν;µ, vanishing on the Lie ..."
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Cited by 5 (4 self)
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The main topic of this paper is two folds. First, we compute the first relative cohomology group of the Lie algebra of smooth vector fields on the projective line, Vect(RP 1), with coefficients in the space of bilinear differential operators that act on tensor densities, Dλ,ν;µ, vanishing on the Lie algebra sl(2, R). Second, we compute the first cohomology group of the Lie algebra sl(2, R) with coefficients in Dλ,ν;µ. 1
Projectively Invariant Cocycles of Holomorphic Vector Fields on an Open Riemann Surface
, 2001
"... Let Σ be an open Riemann surface and Hol(Σ) be the Lie algebra of holomorphic vector fields on Σ. We fix a projective structure (i.e. a local SL2(C)−structure) on Σ. We calculate the first group of cohomology of Hol(Σ) with coefficients in the space of linear holomorphic operators acting on tensor d ..."
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Cited by 5 (4 self)
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Let Σ be an open Riemann surface and Hol(Σ) be the Lie algebra of holomorphic vector fields on Σ. We fix a projective structure (i.e. a local SL2(C)−structure) on Σ. We calculate the first group of cohomology of Hol(Σ) with coefficients in the space of linear holomorphic operators acting on tensor densities, vanishing on the Lie algebra sl2(C). The result is independent on the choice of the projective structure. We give explicit formulæ of 1cocycles generating this cohomology group. 1
Poncin N., Decomposition of symmetric tensor fields in the presence of a flat contact projective structure
 2008), 252–269, math.DG/0703922. Conformally Equivariant Quantization in Dimension 12 11
"... Abstract. Let M be an odddimensional Euclidean space endowed with a contact 1form α. We investigate the space of symmetric contravariant tensor fields over M as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up of those vector fields that preserve the con ..."
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Cited by 5 (1 self)
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Abstract. Let M be an odddimensional Euclidean space endowed with a contact 1form α. We investigate the space of symmetric contravariant tensor fields over M as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up of those vector fields that preserve the contact structure. If we consider symmetric tensor fields with coefficients in tensor densities (also called symbols), the vertical cotangent lift of the contact form α is a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symmetric density valued tensor fields. This generalized Hamiltonian operator on the space of symbols is invariant with respect to the action of the projective contact algebra sp(2n+2). These two operators lead to a decomposition of the space of symbols (except for some critical density weights), which generalizes a splitting proposed by V. Ovsienko in [18]. 1.
Conformal Schwarzian derivatives and conformally invariant quantization
 Internat. Math. Res. Not. 2002
"... Let (M, g) be a pseudoRiemannian manifold. We propose a new approach for defining the conformal Schwarzian derivatives. These derivatives are 1cocycles on the group of diffeomorphisms of M related to the modules of linear differential operators. As operators, these derivatives do not depend on the ..."
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Cited by 4 (4 self)
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Let (M, g) be a pseudoRiemannian manifold. We propose a new approach for defining the conformal Schwarzian derivatives. These derivatives are 1cocycles on the group of diffeomorphisms of M related to the modules of linear differential operators. As operators, these derivatives do not depend on the rescaling of the metric g. In particular, if the manifold (M, g) is conformally flat, these derivatives vanish on the conformal group O(p + 1, q + 1), where dim(M) = p + q. This work is a continuation of [2, 4] where the Schwarzian derivative was defined on a manifold endowed with a projective connection. 1
Geometric invariants of fanning curves
 Adv. Appl. Math
"... Abstract. We study the geometry of an important class of generic curves in the Grassmann manifolds of ndimensional subspaces and Lagrangian subspaces of IR 2n under the action of the linear and linear symplectic groups. ..."
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Cited by 3 (0 self)
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Abstract. We study the geometry of an important class of generic curves in the Grassmann manifolds of ndimensional subspaces and Lagrangian subspaces of IR 2n under the action of the linear and linear symplectic groups.