共查询到20条相似文献,搜索用时 15 毫秒
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The theory of principal G-bundles over a Lie groupoid is an important one unifying various types of principal G-bundles, including those over manifolds, those over orbifolds, as well as equivariant principal G-bundles. In this paper, we study differential geometry of these objects, including connections and holonomy maps. We also
introduce a Chern–Weil map for these principal bundles and prove that the characteristic classes obtained coincide with the
universal characteristic classes. As an application, we recover the equivariant Chern–Weil map of Bott–Tu. We also obtain
an explicit chain map between the Weil model and the simplicial model of equivariant cohomology which reduces to the Bott–Shulman
map when the manifold is a point.
P. Xu Research partially supported by NSF grant DMS-03-06665. 相似文献
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George N. Galanis 《Periodica Mathematica Hungarica》2007,54(1):1-13
A new methodology leading to the construction of a universal connection for Fréchet principal bundles is proposed in this
paper. The classical theory, applied successfully so far for finite dimensional and Banach modelled bundles, collapses within
the framework of Fréchet manifolds. However, based on the replacement of the space of continuous linear mappings by an appropriate
topological vector space, we endow the bundle J
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P of 1-jets of the sections of a Fréchet principal bundle P with a connection form by means of which we may “reproduce” every connection of P.
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XiaoJiang Tan 《中国科学A辑(英文版)》2008,51(4):721-727
In this paper,we give some conditions on the surjective of multiply maps H~0(R,L)×H~0(R,K)→H~0(R,L(?)K).Here R is a compact Riemann surface,L a line bundle on R and K is the canonical line bundle. 相似文献
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Let C be a smooth projective curve, and let G be a reductive algebraic group. We give a necessary condition, in terms of automorphism groups of principal G-bundles on C, for the existence of Poincaré families parameterized by Zariski-open parts of their coarse moduli schemes. Applications are given for the moduli spaces of orthogonal and symplectic bundles. To cite this article: I. Biswas, N. Hoffmann, C. R. Acad. Sci. Paris, Ser. I 347 (2009). 相似文献
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Mathematische Zeitschrift - In this article, we study Newton–Okounkov bodies on projective vector bundles over curves. Inspired by Wolfe’s estimates used to compute the volume function... 相似文献
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Carlos Florentino 《manuscripta mathematica》2001,105(1):69-83
We study a natural map from representations of a free group of rank g in GL(n,ℂ), to holomorphic vector bundles of degree 0 over a compact Riemann surface X of genus g, associated with a Schottky uniformization of X. Maximally unstable flat bundles are shown to arise in this way. We give a necessary and sufficient condition for this map
to be a submersion, when restricted to representations producing stable bundles. Using a generalized version of Riemann's
bilinear relations, this condition is shown to be true on the subspace of unitary Schottky representations.
Received: 13 June 2000 / Revised version: 29 December 2000 相似文献
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S. A. H. Cardona 《Annals of Global Analysis and Geometry》2013,44(4):455-469
We study the basic properties of Higgs sheaves over compact Kähler manifolds and establish some results concerning the notion of semistability; in particular, we show that any extension of semistable Higgs sheaves with equal slopes is semistable. Then, we use the flattening theorem to construct a regularization of any torsion-free Higgs sheaf and show that it is in fact a Higgs bundle. Using this, we prove that any Hermitian metric on a regularization of a torsion-free Higgs sheaf induces an admissible structure on the Higgs sheaf. Finally, using admissible structures we prove some properties of semistable Higgs sheaves. 相似文献
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S. A. H. Cardona 《Annals of Global Analysis and Geometry》2012,42(3):349-370
We review the notions of (weak) Hermitian–Yang–Mills structure and approximate Hermitian–Yang–Mills structure for Higgs bundles. Then, we construct the Donaldson functional for Higgs bundles over compact K?hler manifolds and we present some basic properties of it. In particular, we show that its gradient flow can be written in terms of the mean curvature of the Hitchin–Simpson connection. We also study some properties of the solutions of the evolution equation associated with that functional. Next, we study the problem of the existence of approximate Hermitian–Yang–Mills structures and its relation with the algebro-geometric notion of semistability and we show that for a compact Riemann surface, the notion of approximate Hermitian–Yang–Mills structure is in fact the differential- geometric counterpart of the notion of semistability. Finally, we review the notion of admissible Hermitian structure on a torsion-free Higgs sheaf and define the Donaldson functional for such an object. 相似文献
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We determine a 2-codimensional CR-structure on the slit tangent bundle \(T_0M\) of a Finsler manifold (M, F) by imposing a condition on the almost complex structure \(\Psi \) associated to F when restricted to the structural distribution of a framed f-structure. This condition is satisfied when (M, F) is of scalar flag curvature (particularly flat). In the Riemannian case (M, g) this last condition means that g is of constant curvature. This CR-structure is finally generalized by using one positive parameter but under more difficult conditions. 相似文献
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Yi Li 《Calculus of Variations and Partial Differential Equations》2014,50(3-4):867-882
In this paper we prove a priori estimates for Donaldson equation’s $$\begin{aligned} \omega \wedge (\chi +\sqrt{-1}\partial \bar{\partial }\varphi )^{n-1} =e^{F}(\chi +\sqrt{-1}\partial \bar{\partial }\varphi )^{n}, \end{aligned}$$ over a compact complex manifold \(X\) of complex dimension \(n\) , where \(\omega \) and \(\chi \) are arbitrary Hermitian metrics. Our estimates answer a question of Tosatti-Weinkove (Asian J. Math. 14:19–40, 2010). 相似文献
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Yan XU & Min RU Department of Mathematics Nanjing Normal University Nanjing China Department of Mathematics University of Houston Houston TX USA 《中国科学A辑(英文版)》2007,50(5):683-688
In this paper, we prove a uniqueness theorem for algebraic curves from a compact Riemann surface into complex projective spaces. 相似文献
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