Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · math/0606522

Explicit formula for the natural and projectively equivariant quantization

F. Radoux
View original source ↗Read source document ↗Export metadata ↓

Abstract

In [8], P. Lecomte conjectured the existence of a natural and projectively equivariant quantization. In [1], M. Bordemann proved this existence using the framework of Thomas-Whitehead connections. In [9], we gave a new proof of the same theorem thanks to the Cartan connections. After these works there was no explicit formula for the quantization. In this paper, we give this formula using the formula in terms of Cartan connections given in [9]. This explicit formula constitutes the generalization to any order of the formulae at second and third orders soon published by Bouarroudj in [2] and [3].

Explore related subjects

math.DG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

F. Radoux. 2006-06-21. Explicit formula for the natural and projectively equivariant quantization. https://doi.org/10.1007/s11005-006-0116-0

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Rotational symmetry of complete gradient Einstein-type manifolds with $α=0$ under vanishing conditions on several tensor fields

To provide a unified framework for various geometric solitons, Catino, Mastrolia, Monticelli, and Rigoli introduced gradient Einstein-type manifolds, which include gradient Yamabe solitons, gradient almost Yamabe solitons, gradient $k$-Yamabe solitons and conformal gradient solitons. In this paper, we show that any nontrivial complete four-dimensional gradient Einstein-type manifold with $α=0$, nonnegative scalar curvature, and vanishing Bach tensor is rotationally symmetric. The Bach-flat condition arises naturally in four-dimensional geometry and physics. We prove the main theorem by exploiting the conformal invariance of Bach-flatness and establishing a relation between two functionals. We also provide classification results under vanishing conditions on the Weyl tensor, the Cotton tensor, and the Cao-Chen-type tensor.

math.DG↗
arXiv2026

The min-max width of spheres associated to the distance function

What one obtains when the min-max methods for the distance function are applied on the space of pairs of points of a Riemannian two-sphere? This question is studied in details in the present article. We show that the associated min-max width do not always coincide with half of the length of a simple closed geodesic which is the union of two minimizing geodesics with the same endpoints. Therefore, it is a new geometric invariant. We study the structure of the set of minimizing geodesics joining a pair of points realizing the width, and relationships between this invariant and the diameter. The extrinsic case of an embedded Riemannian sphere is also considered.

math.DG↗
arXiv2026

On the $\mathcal{D}^+_J$ operator on higher-dimensional almost Kähler manifolds

In this paper, we introduce $\mathcal{D}^+_J$, a generalization of $\partial\bar{\partial}$ operator on higher dimensional almost Kähler manifolds. Using the $\mathcal{D}^+_J$ operator, we investigate the $\bar{\partial}$-problem in almost Kähler geometry and explore the generalized Monge-Ampère equation on almost Kähler manifolds. We establish uniqueness up to an additive constant. We also prove a local existence theorem for this equation on almost Kähler four-manifold. At last, we find an elliptical system for $\mathcal{D}^+_J$ operator. As an application, we reorganize the result of Tosatti-Weinkove-Yau in \cite{TWY}.

math.DG↗