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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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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
Remarks on the Conformally Invariant Quantization by means of a Finsler Function
, 2002
"... Let (M, F) be a Finsler manifold. We construct a 1cocycle on Diff(M) with values in the space of differential operators acting on tensor fields, by means of the Finsler function F. This is a first step toward the existence of Schwarzian derivatives for Finsler structure. We, furthermore, discuss so ..."
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Let (M, F) be a Finsler manifold. We construct a 1cocycle on Diff(M) with values in the space of differential operators acting on tensor fields, by means of the Finsler function F. This is a first step toward the existence of Schwarzian derivatives for Finsler structure. We, furthermore, discuss some properties of the conformally invariant quantization map by means of a (Sazaki type) metric on the slit bundle TM\0 induced by F. 1
Cohomology of Groups of Diffeomorphisms Related to the Modules of Differential Operators on a Smooth Manifold
, 2001
"... Let M be a manifold and T ∗ M be the cotangent bundle. We introduce a 1cocycle on the group of diffeomorphisms of M with values in the space of linear differential operators acting on C ∞ (T ∗ M). When M is the ndimensional sphere, S n, we use this 1cocycle to compute the firstcohomology group o ..."
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Let M be a manifold and T ∗ M be the cotangent bundle. We introduce a 1cocycle on the group of diffeomorphisms of M with values in the space of linear differential operators acting on C ∞ (T ∗ M). When M is the ndimensional sphere, S n, we use this 1cocycle to compute the firstcohomology group of the group of diffeomorphisms of S n, with coefficients in the space of linear differential operators acting on contravariant tensor fields. 1
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, 2001
"... Cohomology of groups of diffeomorphisms related to the modules of differential operators on a smooth manifold ..."
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Cohomology of groups of diffeomorphisms related to the modules of differential operators on a smooth manifold
Conformal Schwarzian derivatives on a pseudoRiemannian manifold
, 2001
"... Let (M, g) be a pseudoRiemannian manifold. We propose a new approach for 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 depend only on the conformal ..."
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Let (M, g) be a pseudoRiemannian manifold. We propose a new approach for 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 depend only on the conformal class 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 [1, 3] where the Schwarzian derivative was defined on a manifold endowed with a projective connection. 1