Hasil untuk "math.DG"

Claus Gerhardt

H. Nguyen

F. Radoux

Lecomte (Prog Theor Phys Suppl 144:125–132, 2001) conjectured the existence of a natural and conformally invariant quantization. In Mathonet and Radoux (Existence of natural and conformally invariant quantizations of arbitrary symbols, math.DG 0811.3710), we gave a proof of this theorem thanks to the theory of Cartan connections. In this paper, we give an explicit formula for the natural and conformally invariant quantization of trace-free symbols thanks to the method used in Mathonet and Radoux and to tools already used in Radoux [Lett Math Phys 78(2):173–188, 2006] in the projective setting. This formula is extremely similar to the one giving the natural and projectively invariant quantization in Radoux.

N. L. Youssef, S. H. Abed, A. Soleiman

The aim of the present paper is to provide an intrinsic investigation of projective changes in Finsler geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained. Nontrivial characterizations of projective changes are given. The fundamental projectively invariant tensors, namely, the projective deviation tensor, the Weyl torsion tensor, the Weyl curvature tensor and the Douglas tensor are investigated. The properties of these tensors and their interrelationships are obtained. Projective connections and projectively flat manifolds are characterized. The present work is entirely intrinsic (free from local coordinates) (arXiv:0904.1602 [math.DG]).

R. Pérez, J. M. Masqué

Paul Koerber

E. Caponio, M. Javaloyes

This paper has been withdrawn by the authors because it has been merged with paper arXiv:0903.3501v1 [math.DG]

A. Vinogradov, L. Vitagliano

We describe the first term of the $\Lambda_{k-1}\mathcal{C}$--spectral sequence (see math.DG/0610917) of the diffiety (E,C), E being the infinite prolongation of an l-normal system of partial differential equations, and C the Cartan distribution on it.

Yuhao Yan

We study the equation $\Delta_g u -\frac{n-2}{4(n-1)}R(g)u+Ku^p=0 (1+\zeta \leq p \leq \frac{n+2}{n-2})$ on locally conformally flat compact manifolds $(M^n,g)$. We prove the following: (i) When the scalar curvature $R(g)>0$ and the dimension $n \geq 4$, under suitable conditions on $K$, all positive solutions $u$ have uniform upper and lower bounds; (ii) When the scalar curvature $R(g)\equiv 0$ and $n \geq 5$, under suitable conditions on $K$, all positive solutions $u$ with bounded energy have uniform upper and lower bounds. We also give an example to show that the energy bound condition for the uniform estimates in math.DG/0602636 is necessary.

A. Vinogradov, L. Vitagliano

In the preceding note math.DG/0610917 the $\Lambda_{k-1}\mathcal{C}$--spectral sequence, whose first term is composed of \emph{secondary iterated differential forms}, was constructed for a generic diffiety. In this note the zero and first terms of this spectral sequence are explicitly computed for infinite jet spaces. In particular, this gives an explicit description of secondary covariant tensors on these spaces and some basic operations with them. On the basis of these results a description of the $\Lambda_{k-1}\mathcal{C}$--spectral sequence for infinitely prolonged PDE's will be given in the subsequent note.

T. Mochizuki

Let $L$ be a local system on a smooth quasi projective variety over $\cnum$. We see that $L$ is semisimple if and only if there exists a tame pure imaginary pluri-harmonic metric on $L$. Although it is a rather minor refinement of a result of Jost and Zuo, it is significant for the study of harmonic bundles and pure twistor $D$-modules. As one of the application, we show that the semisimplicity of local systems are preserved by the pull back via a morphism of quasi projective varieties. This paper will be included as an appendix to our previous paper, ``Asymptotic behaviour of tame harmonic bundles and an application to pure twistor $D$-modules'', math.DG/0312230. Keywords: Higgs fields, harmonic bundle, semisimple local system.

M. Olbrich

This paper contains a thorough investigation of invariant distributions supported on limit sets of discrete groups acting convex cocompactly on symmetric spaces of negative curvature. It can be considered as a continuation of math.DG/9810146. Based on this investigation we provide proofs of the Hodge theoretic results for the cohomology of real hyperbolic manifolds announced in math.DG/0009038, improve the bounds for the critical exponents obtained by Corlette for the quaternionic and the Cayley case, compute the L^2-cohomology for the corresponding locally symmetric spaces, prove a version of the Harder-Borel conjecture for real hyperbolic manifolds, and compute higher cohomology groups with coefficients in hyperfunctions supported on the limit set.

F. Radoux

Abstract In [C. Duval, V. Ovsienko, Projectively equivariant quantization and symbol calculus: Noncommutative hypergeometric functions, Lett. Math. Phys. 57 (1) (2001) 61–67], the authors showed the existence and the uniqueness of a s l ( m + 1 , R ) -equivariant quantization in non-critical situations. The curved generalization of the s l ( m + 1 , R ) -equivariant quantization is the natural and projectively equivariant quantization. In [M. Bordemann, Sur l’existence d’une prescription d’ordre naturelle projectivement invariante (submitted for publication). math.DG/0208171 ] and [Pierre Mathonet, Fabian Radoux, Natural and projectively equivariant quantizations by means of Cartan connections, Lett. Math. Phys. 72 (3) (2005) 183–196], the existence of such a quantization was proved in two different ways. In this paper, we show that this quantization is not unique.

Christoph Wockel

This paper has been withdrawn by the author. The content of the previous versions is now covered by the more recent papers - math.DG/0610252 (concerning the Lie group structuren on the gauge groups) - math.DG/0612522 (concerning the weak homotopy equivalence) - math.AT/0511404 (concerning the homotopy groups of gauge groups)

Alain Berthomieu

This is the final part of the work started in math.DG/0611281 and math.DG/0703916. Here the question of double fibration ois adressed both for relative k-theory and free multiplicative K-theory. In the case of relative and ``nonfree'' multiplicative K-theory, the direct image is proved to be functorial for double submersions.

F. Hélein

The purpose of this short note is to relate a representation formula due to the Author and P. Romon for Lagrangian surfaces (see math.DG/0009202) to a more general Weierstrass representation type formula found by Konopelchenko for surfaces in 4-dimensional space (see math.DG/9807129). Simplifications are pointed out.

J. Merker

In this paper, a direct continuation of math.DG/0411165, we generalize S. Lie's linearization criterion of an ordinary second order differential equation to the case of several independent variables (x^1, x^2 ..., x^n), n >1, and a single dependent variable y. Strikingly, as in math.DG/0411165, the (complicated) characterizing differential system is of first order. By means of computer programming, this phenomenon was discovered in the case n=2 by S. Neut and M. Petitot (www.lifl.fr/~neut/recherche/these.pdf).

A. Vinogradov, L. Vitagliano

A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.

M. Guest

Although this article can be read independently, it is a continuation of the introduction to integrable systems aspects of quantum cohomology given in part 1 (math.DG/0104274). In the same elementary style, i.e. assuming basic properties of quantum cohomology and concentrating on the simplest nontrivial examples, the quantum differential equations of Givental are studied in some detail. The solutions are described first as generating functions for certain Gromov-Witten invariants, then as generalizations of hypergeometric functions, as predicted by the Mirror Theorem.

F. Radoux

In [Prog Theor Phys Suppl 49(3):173–196, 1999], Lecome conjectured the existence of a natural and projectively equivariant quantization. In [math.DG/0208171, Submitted], Bordemann proved this existence using the framework of Thomas–Whitehead connections. In [Lett Math Phys 72(3):183–196, 2005], 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 [Lett Math Phys 72(3):183–196, 2005]. This explicit formula constitutes the generalization to any order of the formulae at second and third orders soon published by Bouarroudj in [Lett Math Phys 51(4):265–274, 2000] and [C R Acad Sci Paris Sér I Math 333(4):343–346, 2001].