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31.
We study Yang-Mills connections on holomorphic bundles over complex K?hler manifolds of arbitrary dimension, in the spirit
of Hitchin's and Simpson's study of flat connections. The space of non-Hermitian Yang-Mills (NHYM) connections has dimension
twice the space of Hermitian Yang-Mills connections, and is locally isomorphic to the complexification of the space of Hermitian
Yang-Mills connections (which is, by Uhlenbeck and Yau, the same as the space of stable bundles). Further, we study the NHYM
connections over hyperk?hler manifolds. We construct direct and inverse twistor transform from NHYM bundles on a hyperk?hler
manifold to holomorphic bundles over its twistor space. We study the stability and the modular properties of holomorphic bundles
over twistor spaces, and prove that work of Li and Yau, giving the notion of stability for bundles over non-K?hler manifolds,
can be applied to the twistors. We identify locally the following two spaces: the space of stable holomorphic bundles on a
twistor space of a hyperk?hler manifold and the space of rational curves in the twistor space of the ‘Mukai’ dual hyperk?hler
manifold. 相似文献
32.
For a symplectic manifold with quantizing line bundle, a choice of almost complex structure determines a Laplacian acting on tensor powers of the bundle. For high tensor powers Guillemin–Uribe showed that there is a well-defined cluster of low-lying eigenvalues, whose distribution is described by a spectral density function. We give an explicit computation of the spectral density function, by constructing certain quasimodes on the associated principle bundle. 相似文献
33.
Robert Laterveer 《数学学报(英文版)》2017,33(7):887-898
This note is about the Chow groups of a certain family of smooth cubic fourfolds. This family is characterized by the property that each cubic fourfold X in the family has an involution such that the induced involution on the Fano variety F of lines in X is symplectic and has a K3 surface S in the fixed locus. The main result establishes a relation between X and S on the level of Chow motives. As a consequence, we can prove finite-dimensionality of the motive of certain members of the family. 相似文献
34.
In this paper, the parakähler Hom-Lie algebras or phase space of Hom-Lie algebras in terms of Hom-left-symmetric algebras are studied. A structure theory of parakähler Hom-Lie algebras in terms of matched pairs of Hom-Lie algebras is also presented. Besides, the bimodules of Hom-left-symmetric algebras are investigated. Furthermore, Hom-left-symmetric bialgebra which is precisely equivalent to parakähler Hom-Lie algebra is introduced. Especially, the coboundary Hom-left-symmetric bialgebra is considered. 相似文献
35.
36.
We consider the problem of existence of constant scalar curvature Kähler metrics on complete intersections of sections of vector bundles. In particular we give general formulas relating the Futaki invariant of such a manifold to the weight of sections defining it and to the Futaki invariant of the ambient manifold. As applications we give a new Mukai–Umemura–Tian like example of Fano 5-fold admitting no Kähler–Einstein metric, and a strong evidence of K-stability of complete intersections in Grassmannians. 相似文献
37.
证明6维严格近凯勒流形中的二阶平行拉格朗日子流形一定是全测地的,这推广了L.Vrancken等人文中的一个重要结果.特别地,得到了齐性近凯勒S3×S3中该类拉格朗日子流形的完全分类. 相似文献
38.
It is well known that any symplectic manifold (M,Ω) has an almost complex structure J which is compatible with Ω. In this paper, we deal with the existence of compatible pairs (J,Ω) on nilpotent Lie algebras
of dimension ≤6, J being an integrable almost complex structure. We prove that if such a pair exists, J must satisfy some extra conditions, namely J must be nilpotent in the sense of [Trans. Am. Math. Soc. 352 (2000) 5405]. Associated to any such a compatible pair, there is a pseudo-Kähler metric g which cannot be positive definite unless
be abelian. All these metrics are Ricci flat, although many of them are nonflat, and we study the behaviour of its curvature tensor under deformation. 相似文献
39.
Paul-Andi Nagy 《Mathematische Zeitschrift》2006,254(1):199-218
Motivated by understanding the limiting case of a certain systolic inequality we study compact Riemannian manifolds having all harmonic 1-forms of constant length. We give complete characterizations as far as Kähler and hyperbolic geometries are concerned. In the second part of the paper, we give algebraic and topological obstructions to the existence of a geometrically 2-formal Kähler metric, at the level of the second cohomology group. A strong interaction with almost Kähler geometry is to be noted. In complex dimension 3, we list all the possible values of the second Betti number of a geometrically 2-formal Kähler metric. 相似文献
40.
Myong-Hee Sung 《Annals of Global Analysis and Geometry》1997,15(6):509-518
We construct Kähler metrics of positive scalar curvature on almost all blown-up ruled surfaces of arbitrary genus. The metrics have an explicit form on ruled surfaces blown up at most twice successively from a minimal model. Our surfaces are generic in the sense that they make up a dense set in the deformations of a given ruled surface. 相似文献