共查询到20条相似文献,搜索用时 62 毫秒
1.
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.
2.
Valentino Tosatti 《Proceedings of the American Mathematical Society》2007,135(12):3985-3988
We prove that a Kähler metric in the anticanonical class, that is a critical point of the functional and has nonnegative Ricci curvature, is necessarily Kähler-Einstein. This partially answers a question of X.X. Chen.
3.
Jian Song 《Transactions of the American Mathematical Society》2005,357(1):45-57
The global holomorphic -invariant introduced by Tian is closely related to the existence of Kähler-Einstein metrics. We apply the result of Tian, Yau and Zelditch on polarized Kähler metrics to approximate plurisubharmonic functions and compute the -invariant on for .
4.
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).
5.
Razvan Veliche 《Proceedings of the American Mathematical Society》2007,135(5):1441-1447
The goal of this note is to prove that the mapping class groups of closed orientable surfaces of genus 2 (with punctures) are not Kähler. An application to compactifications of the moduli space of genus curves (with punctures) is given.
6.
Leon Takhtajan Peter Zograf 《Transactions of the American Mathematical Society》2003,355(5):1857-1867
We show that the real-valued function on the moduli space of pointed rational curves, defined as the critical value of the Liouville action functional on a hyperbolic -sphere with conical singularities of arbitrary orders , generates accessory parameters of the associated Fuchsian differential equation as their common antiderivative. We introduce a family of Kähler metrics on parameterized by the set of orders , explicitly relate accessory parameters to these metrics, and prove that the functions are their Kähler potentials.
7.
M. J. Slupinski 《Transactions of the American Mathematical Society》2003,355(5):2011-2046
By a uniform abstract procedure, we obtain integrated forms of the classical Hodge identities for Riemannian, Kähler and hyper-Kähler manifolds, as well as of the analogous identities for metrics of arbitrary signature. These identities depend only on the type of geometry and, for each of the three types of geometry, define a multiplicative functor from the corresponding category of real, graded, flat vector bundles to the category of infinite-dimensional -projective representations of an algebraic structure. We define new multiplicative numerical invariants of closed Kähler and hyper-Kähler manifolds which are invariant under deformations of the metric.
8.
Xu-Qian Fan 《Proceedings of the American Mathematical Society》2007,135(1):289-298
In this paper, we will study the problem of uniqueness of Kähler Ricci flow on some complete noncompact Kähler manifolds and the convergence of the flow on with the initial metric constructed by Wu and Zheng.
9.
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 .
10.
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.
11.
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.
12.
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.
13.
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.
14.
N. Anghel 《Proceedings of the American Mathematical Society》2005,133(8):2461-2467
We use separation of variables for generalized Dirac operators on rotationally symmetric Riemannian manifolds to recover a theorem of Dodziuk regarding the spaces of -harmonic forms on such manifolds.
15.
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.
16.
In this article, we use the pluricomplex Green function to give a sufficient condition for the existence and the completeness of the Bergman metric. As a consequence, we proved that a simply connected complete Kähler manifold possesses a complete Bergman metric provided that the Riemann sectional curvature , which implies a conjecture of Greene and Wu. Moreover, we obtain a sharp estimate for the Bergman distance on such manifolds. 相似文献
17.
Operators of the form with a pseudodifferential symbol belonging to the Hörmander class , , , and certain perturbations are shown to possess a bounded -calculus in Besov-Triebel-Lizorkin and certain subspaces of Hölder spaces, provided is suitably elliptic. Applications concern pseudodifferential operators with mildly regular symbols and operators on manifolds of low regularity. An example is the Dirichlet-Neumann operator for a compact domain with -boundary.
18.
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.
19.
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.
20.
Dans cette note, on montre que les courbes, lisses connexes, de degré et genre , tracées sur une surface quartique normale variable de , et n'y étant pas intersection complète, forment des familles de dimensions . Cette majoration est la meilleure possible. Comme application on prouve que le schéma de Hilbert des courbes lisses connexes de de degré et genre est irréductible.