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Rafael María Rubio Ruiz 《manuscripta mathematica》2001,105(3):323-342
By differentiability we means C
∞ differentiability. Recall that the span of a manifold M is the maximum number of linearly independent vector fields in every
point. The aim of this paper is to relate the span of M with the minimal dimension of the orbits of a differentiable action ϕ:ℝ
n
×M→M that keeps a contact structure.
Received: 19 July 2000 / Revised version: 20 April 2001 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(6):659-663
We prove the following theorems:
- 1)Any surgery of index one on u tight contact manifold (of dimension three) gives rise to a manifold which carries a natural tight contact structure.
- 2)In a tight contact manifold, any two isotopic spheres which carry the same characteristic foliation are isotopic through a contact isolopy.
- 3)In a tight contact manifold, any two isotopic spheres have isomorphic complements.
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《Journal of Functional Analysis》1987,71(1):182-194
If P′ is a C∞ positive function on a compact riemannian manifold of dimension n ⩾ 3 and metric g, we define a conformal invariant v(R′) and we prove that if v(R′) is small enough, R′ is the scalar curvature of the manifold endowed with a metric conformal to g. Then we are interested in the case of the sphere Sn and finally in Yamabe's problem. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(11):1031-1033
Let (V2, g) be a C∞ compact Riemannian manifold of negative scalar curvature of dimension 2, and let f be a C∞ function defined on V2. We intend to find a condition on f in order that f be the scalar curvature of a metric conformal to the initial metric g. 相似文献
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Antoine Ducros 《manuscripta mathematica》2001,105(3):311-321
Let V be an henselian discrete valuation ring with real closed residue field and let k be its quotient ring; we denote by k + and k − the two real closures of k. Consider a k-abelian variety A. We compute the Galois-cohomology group H 1(k,A) in terms of the reduction of the dual variety of A and of the semi-algebraic topology of A(k +) and A(k −). The tools we need are Ogg's results concerning valuation rings with algebraically closed residue field, Hochschild–Serre spectral sequence and Scheiderer's local-global principles. At the end we study more precisely the case of an elliptic curve. Received: 23 October 2000 相似文献
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André Haefliger 《Commentarii Mathematici Helvetici》1962,36(1):47-82
Sans résumé
This work was partially supported by NSF Grant G-10.700. 相似文献
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Nicolas Perrin 《manuscripta mathematica》2005,116(4):449-474
In the first part, we give some necessary conditions for a torsion free sheaf on a smooth threefold to be a reduced limit of vector bundles.In a second part of the article, we illustrate these results by reinterpreting a condition described by G. Ellingsrud and S.A. Strømme as a condition obtained in the first part. This enables us to identify, in a well known too big familly, the torsion free sheaves that are limit of vector bundles. 相似文献
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Résumé. Dans cet article, nous nous proposons d'étudier quelques problèmes d'analyse sur les variétés cuspidales, par exemple, la fonction maximale de Hardy-Littlewood, l'estimation en temps petit du noyau de la chaleur ainsi que de son gradient, et aussi les transformées de Riesz.Mathematics Subject Classification (2000): 58J35, 42B20, 42B25 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》2001,332(4):299-304
Let (M,J) be an almost complex manifold. By using local coordinate system adapted to the structure J, we prove that every closed positive current on M possesses a Lelong number at any point. In case the manifold is equipped with an integrable complex structure, this Lelong number coincides with the usual Lelong number of a closed positive current. 相似文献
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Christine Laurent-Thiebaut 《Annali di Matematica Pura ed Applicata》1988,150(1):141-151
Sumé Etant donné un domaine D relativement compact d'une variété de Stein M de dimension n, n 2, on montre que toute fonction continue, CR, définie sur un ouvert connexe de D ayant un complémentaire K dont l'enveloppe holomorphiquement convexe dans M ne rencontre pas ¯ DK, se prolonge en une fonction holomorphe sur D.
Summary Let there be given a relatively compact domain D in a Stein manifold M of dimension n, n 2, we prove the holomorphic extendibility of the continuous CR functions defined on an open connected subset of D, provided theO(M)-hull of its complementary K does not meet ¯ DK.相似文献
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Nefton Pali 《manuscripta mathematica》2005,118(3):311-337
If (X, J) is an almost complex manifold, then a function u is said to be plurisubharmonic on X if it is upper semi-continuous and its restriction to every local pseudo-holomorphic curve is subharmonic. As in the complex
case, it is conjectured that plurisubharmonicity is equivalent to the positivity of the (1,1)-current , (the (1,1)-current need not be closed here!). The conjecture is trivial if u is of class The result is elementary in the complex integrable case because the operator can be written as an operator with constant coefficients in complex coordinates. Hence the positivity of the current is preserved
by regularising with usual convolution kernels. This is not possible in the almost complex non integrable case and the proof
of the result requires a much more intrinsic study. In this chapter we prove the necessity of the positivity of the (1,1)-current
. We prove also the sufficiency of the positivity in the particular case of an upper semi-continuous function f which is continuous in the complement of the singular locus f−1(−∞).
Résume Une fonction semi-continue supérieurement u sur une variété presque complexe (X, J) est dite plurisousharmonique si la restriction à toute courbe pseudo-holomorphe locale est sous-harmonique. Comme dans le cas analytique complexe, nous conjecturons que la notion de plurisousharmonicité pour une fonction u est équivalente à la positivité du (1,1)-courant , (lequel n'est pas forcément fermé dans le cas non intégrable). La conjecture est triviale dans le cas d'une fonction u de classe Le résultat en question est élémentaire dans le cas complexe intégrable car l'opérateur s'écrit comme un opérateur à coefficients constants dans des coordonnées complexes. On peut donc facilement conserver la positivité du courant en régularisant avec des noyaux usuels. Dans le cas presque complexe non intégrable ceci ce n'est pas possible et la preuve du résultat exige un étude beaucoup plus intrinsèque. Nous montrons la nécessité de la positivité du (1,1)-courant en utilisant la théorie locale des courbes J-holomorphes. Nous montrons aussi la suffisance de la positivité dans le cas particulier d'une fonction f semi-continue supérieurement et continue en dehors du lieu singulier f−1(−∞).相似文献