共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
Holomorphic projective structures on compact complex surfaces 总被引:2,自引:0,他引:2
3.
4.
5.
A. V. Vasin 《Journal of Mathematical Sciences》2000,101(3):3053-3059
A sheaf of differentials on a compact Riemann surface supplied with a projective structure is said to be n-analytic if, in
local projective coordinates, sections of the sheaf satisfy the differential equation {
} For the projective structure induced by a covering mapping from the disk, an explicit characterization of the space of cross
sections and of the space of first cohomologies of an n-analytic sheaf is given in terms of known spaces of sections of certain
holomorphic sheaves. Bibliography: 10 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 15–25.
Translated by S. V. Kislyakov. 相似文献
6.
7.
Barbara Opozda 《Proceedings of the American Mathematical Society》2004,132(9):2713-2721
Global properties of locally homogeneous and curvature homogeneous affine connections are studied. It is proved that the only locally homogeneous connections on surfaces of genus different from 1 are metric connections of constant curvature. There exist nonmetrizable nonlocally symmetric locally homogeneous affine connections on the torus of genus 1. It is proved that there is no global affine immersion of the torus endowed with a nonflat locally homogeneous connection into .
8.
9.
Letν′ be the complementary in a compact Riemann surface ν of a point (or a finite set). In this paper are characterized the subfields,
of the field of meromorphic functions inν′, containing sufficient functions to verify a factorization property, similar to that of the classical Weierstrass theorem.
It is also seen that the field generated by the Baker functions is not of this type, and the problem is solved of determining
the divisors, inν′, of the holomorphic functions admiting Weierstrass factorizations with Baker functions as factors. As an application, a
theorem is obtained characterizing the infinite products, of meromorphic functions in ν with bounded degree, which converge
normally inν′.
The first-named author is partially supported by PB91-0188. 相似文献
10.
《复变函数与椭圆型方程》2012,57(15):1163-1164
Let X be a smooth and connected Riemann surface of genus g 0 and f: X P1, h: X P1 non-constant meromorphic functions on X. Fix an integer n 4 and assume the existence of n distinct points a1, , an P1 such that [image omitted] (set-theoretically) for every i. Here we prove that either f = h or [image omitted]. 相似文献
11.
We consider a period map from Teichmüller space to
, which is a real vector bundle over the Siegel upper half space. This map lifts the Torelli map. We study the action of the mapping class group on this period map. We show that the period map from Teichmüller space modulo the Johnson kernel is generically injective. We derive relations that the quadratic periods must satisfy. These identities are generalizations of the symmetry of the Riemann period matrix. Using these higher bilinear relations, we show that the period map factors through a translation of the subbundle
and is completely determined by the purely holomorphic quadratic periods. We apply this result to strengthen some theorems in the literature. One application is that the quadratic periods, along with the abelian periods, determine a generic marked compact Riemann surface up to an element of the kernel of Johnson's homomorphism. Another application is that we compute the cocycle that exhibits the mapping class group modulo the Johnson kernel as an extension of the group SP
g
() by the group
. 相似文献
12.
Yi-Hu Yang 《Calculus of Variations and Partial Differential Equations》2008,32(4):411-427
We apply the Dirichlet’s principle to a modified energy functional on Riemann surfaces to reprove the existence of harmonic
metrics with certain prescribed singularities due to Simpson, Sabbah and Biquard–Boalch, and hence of differentials with twisted
coefficients of the second and third kinds. As a by-product, this generalizes the classical theory of Abelian differentials
on a compact Riemann surface to the case of twisted coefficients. This also proposes a more natural approach for general existence
of harmonic metrics in the higher dimensional case.
The author supported partially by NSF of China (No. 10471105, 10771160). 相似文献
13.
Emilio Bujalance F. J. Cirre Marston Conder 《Transactions of the American Mathematical Society》2003,355(4):1537-1557
The question of whether a given group which acts faithfully on a compact Riemann surface of genus is the full group of automorphisms of (or some other such surface of the same genus) is considered. Conditions are derived for the extendability of the action of the group in terms of a concrete partial presentation for associated with the relevant branching data, using Singerman's list of signatures of Fuchsian groups that are not finitely maximal. By way of illustration, the results are applied to the special case where is a non-cyclic abelian group.
14.
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
15.
16.
17.
Andreas Schweizer 《Archiv der Mathematik》2005,84(1):71-78
Let S be a compact Riemann surface of genus g and gonality d. We derive upper bounds (in terms of g and/or d) for the number of values that two non-constant meromorphic functions on S can share. The case d = 2 (i.e., the surface is hyperelliptic or elliptic) is studied in more detail.Received: 14 April 2004 相似文献
18.
Ulrich Oertel 《Indagationes Mathematicae》2004,15(2):269-282
In this paper, we introduce two new kinds of structures on a non-compact surface: broken hyperbolic structures and broken measured foliations. The space of broken hyperbolic structures contains the Teichmüller space of the surface as a subspace. The space of broken measured foliations is naturally identified with the space of affine foliations of the surface. We describe a topology on the union of the space of broken hyperbolic structures and of the space of broken measured foliations which generalizes Thurston's compactification of Teichmüller space. 相似文献
19.
20.