共查询到20条相似文献,搜索用时 31 毫秒
1.
Eric Mortenson 《Transactions of the American Mathematical Society》2003,355(3):987-1007
Fernando Rodriguez-Villegas has conjectured a number of supercongruences for hypergeometric Calabi-Yau manifolds of dimension . For manifolds of dimension , he observed four potential supercongruences. Later the author proved one of the four. Motivated by Rodriguez-Villegas's work, in the present paper we prove a general result on supercongruences between values of truncated hypergeometric functions and Gaussian hypergeometric functions. As a corollary to that result, we prove the three remaining supercongruences.
2.
Eugene Lerman 《Transactions of the American Mathematical Society》2004,356(10):4075-4083
Contact toric manifolds of Reeb type are a subclass of contact toric manifolds which have the property that they are classified by the images of the associated moment maps. We compute their first and second homotopy group terms of the images of the moment map. We also explain why they are -contact.
3.
Roger Bielawski 《Transactions of the American Mathematical Society》2006,358(9):3997-4019
We study manifolds arising as spaces of sections of complex manifolds fibering over with the normal bundle of each section isomorphic to .
4.
Xiaodong Wang 《Proceedings of the American Mathematical Society》2007,135(9):2949-2960
We discuss a class of complete Kähler manifolds which are asymptotically complex hyperbolic near infinity. The main result is a sharp vanishing theorem for the second cohomology of such manifolds under certain assumptions. The borderline case characterizes a Kähler-Einstein manifold constructed by Calabi.
5.
Martin Scharlemann Abigail Thompson 《Proceedings of the American Mathematical Society》2005,133(6):1573-1580
Understanding non-Haken -manifolds is central to many current endeavors in -manifold topology. We describe some results for closed orientable surfaces in non-Haken manifolds, and extend Fox's theorem for submanifolds of the 3-sphere to submanifolds of general non-Haken manifolds. In the case where the submanifold has connected boundary, we show also that the -connected sum decomposition of the submanifold can be aligned with such a structure on the submanifold's complement.
6.
Alex N. Dranishnikov Yuli B. Rudyak 《Proceedings of the American Mathematical Society》2005,133(5):1557-1561
We construct closed -connected manifolds of dimensions that possess non-trivial rational Massey triple products. We also construct examples of manifolds such that all the cup-products of elements of vanish, while the group is generated by Massey products: such examples are useful for the theory of systols.
7.
Ailana Fraser 《Proceedings of the American Mathematical Society》2007,135(11):3733-3744
We prove Morse index estimates for the area functional for minimal surfaces that are solutions to the free boundary problem in -convex domains in manifolds of nonnegative complex sectional curvature.
8.
Tobias Ekholm John Etnyre Michael Sullivan 《Transactions of the American Mathematical Society》2007,359(7):3301-3335
A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form , where is an exact symplectic manifold, is established. The class of such contact manifolds includes 1-jet spaces of smooth manifolds. As an application, contact homology is used to provide (smooth) isotopy invariants of submanifolds of and, more generally, invariants of self transverse immersions into up to restricted regular homotopies. When , this application is the first step in extending and providing a contact geometric underpinning for the new knot invariants of Ng.
9.
Pedro Ontaneda 《Transactions of the American Mathematical Society》2003,355(3):935-965
We give examples of non-compact finite volume real hyperbolic manifolds of dimension greater than five, such that their doubles admit at least three non-equivalent smoothable structures, two of which admit a Riemannian metric of non-positive curvature while the third does not. We also prove that the doubles of non-compact finite volume real hyperbolic manifolds of dimension greater than four are differentiably rigid. 相似文献
10.
Mahta Khosravi Yiannis N. Petridis 《Proceedings of the American Mathematical Society》2005,133(12):3561-3571
We prove that the error term in Weyl's law for `rational' -dimensional Heisenberg manifolds is of order . In the `irrational' case, for generic -dimensional Heisenberg manifolds with 1$">, we prove that the error term is of the order . The polynomial growth is optimal.
11.
Pierre Guerini Alessandro Savo 《Transactions of the American Mathematical Society》2004,356(1):319-344
We study the gap of the first eigenvalue of the Hodge Laplacian acting on -differential forms of a manifold with boundary, for consecutive values of the degree .
We first show that the gap may assume any sign. Then we give sufficient conditions on the intrinsic and extrinsic geometry to control it. Finally, we estimate the first Hodge eigenvalue of manifolds whose boundaries have some degree of convexity.
12.
Fuquan Fang Sé rgio Mendonç a 《Transactions of the American Mathematical Society》2005,357(9):3725-3738
The main purpose of this paper is to prove several connectedness theorems for complex immersions of closed manifolds in Kähler manifolds with positive holomorphic -Ricci curvature. In particular this generalizes the classical Lefschetz hyperplane section theorem for projective varieties. As an immediate geometric application we prove that a complex immersion of an -dimensional closed manifold in a simply connected closed Kähler -manifold with positive holomorphic -Ricci curvature is an embedding, provided that . This assertion for follows from the Fulton-Hansen theorem (1979).
13.
Kensho Takegoshi 《Proceedings of the American Mathematical Society》2003,131(9):2849-2858
A non -integrability condition of non-constant non-negative subharmonic functions on a general complete manifold is given in an optimal form. As an application in differential geometry, several topics related to parabolicity of manifolds, the Liouville theorem for harmonic maps and conformal deformation of metrics are shown without any assumption on the Ricci curvature of .
14.
Eduardo Gonzalez 《Transactions of the American Mathematical Society》2006,358(7):2927-2948
This paper studies symplectic manifolds that admit semi-free circle actions with isolated fixed points. We prove, using results on the Seidel element, that the (small) quantum cohomology of a -dimensional manifold of this type is isomorphic to the (small) quantum cohomology of a product of copies of . This generalizes a result due to Tolman and Weitsman.
15.
Shusen Ding 《Proceedings of the American Mathematical Society》2004,132(8):2367-2375
In this paper, we first prove the local two-weight Caccioppoli inequalities for solutions to the nonhomogeneous -harmonic equation of the form . Then, as applications of the local results, we prove the global two-weight Caccioppoli-type inequalities for these solutions on Riemannian manifolds.
16.
Adam S. Sikora 《Transactions of the American Mathematical Society》2005,357(5):2007-2020
We investigate the relations between the cut number, and the first Betti number, of -manifolds We prove that the cut number of a ``generic' -manifold is at most This is a rather unexpected result since specific examples of -manifolds with large and are hard to construct. We also prove that for any complex semisimple Lie algebra there exists a -manifold with and Such manifolds can be explicitly constructed.
17.
We compute the curvature of the -metric on the direct image of a family of Hermitian holomorphic vector bundles over a family of compact Kähler manifolds. As an application, we show that the -metric on the direct image of a family of ample line bundles over a family of abelian varieties and equipped with a family of canonical Hermitian metrics is always projectively flat. When the parameter space is a compact Kähler manifold, this leads to the poly-stability of the direct image with respect to any Kähler form on the parameter space.
18.
L. Godinho 《Transactions of the American Mathematical Society》2006,358(11):4919-4933
A theorem of Tolman and Weitsman states that all symplectic semifree circle actions with isolated fixed points on compact symplectic manifolds must be Hamiltonian and have the same equivariant cohomology and Chern classes of equipped with the standard diagonal circle action. In this paper, we show that the situation is much different when we consider compact symplectic orbifolds. Focusing on -orbifolds with isolated cone singularities, we show that such actions, besides being Hamiltonian, can now be obtained from either or a weighted projective space, or a quotient of one of these spaces by a finite cyclic group, by a sequence of special weighted blow-ups at fixed points. In particular, they can have any number of fixed points.
19.
Hong-Quan Li Noë l Lohoue 《Transactions of the American Mathematical Society》2003,355(2):689-711
We prove R. Strichartz's estimates for solutions of the wave equation on some conical manifolds. RÉSUMÉ. On prouve des estimations pour les solutions de l'équation des ondes, analogues aux estimations de R. Strichartz, sur certaines variétés coniques.
20.
Emil J. Straube Marcel K. Sucheston 《Transactions of the American Mathematical Society》2003,355(1):143-154
Boas and Straube proved a general sufficient condition for global regularity of the -Neumann problem in terms of families of vector fields that commute approximately with . In this paper, we study the existence of these vector fields on a compact subset of the boundary whose interior is foliated by complex manifolds. This question turns out to be closely related to properties of interest from the point of view of foliation theory.