共查询到20条相似文献,搜索用时 156 毫秒
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Debraj Chakrabarti 《Journal of Geometric Analysis》2008,18(3):720-739
We give examples of non-smooth sets in the complex plane with the property that every holomorphic map continuous to the boundary
from these sets into any complex manifold may be uniformly approximated by maps holomorphic in some neighborhood of the set
(Mergelyan-type approximation for manifold-valued maps.) Similar results are proved for sections of complex-valued holomorphic
submersions from complex manifolds.
相似文献
3.
Sorin Dumitrescu 《Monatshefte für Mathematik》2010,19(2):145-154
We study local automorphisms of holomorphic Cartan geometries. This leads to classification results for compact complex manifolds admitting holomorphic Cartan geometries. We prove that a compact Kähler Calabi–Yau manifold bearing a holomorphic Cartan geometry of algebraic type admits a finite unramified cover which is a complex torus. 相似文献
4.
E. M. Chirka 《Proceedings of the Steklov Institute of Mathematics》2012,279(1):194-206
We prove some generalizations and analogs of the Harnack inequalities for pluriharmonic, holomorphic and “almost holomorphic” functions. The results are applied to proving smoothness properties of holomorphic motions over almost complex manifolds. 相似文献
5.
We investigate relative holomorphic connections on a principal bundle over a family of compact complex manifolds. A sufficient condition is given for the existence of a relative holomorphic connection on a holomorphic principal bundle over a complex analytic family. We also introduce the notion of relative equivariant bundles and establish its relation with relative holomorphic connections on principal bundles. 相似文献
6.
复Banach空间中C-R方程的全纯解 总被引:3,自引:0,他引:3
二重复数是复数的一种推广,在其上的全纯映照族对应于C2上满足复Cauchy-Riemann方程的全纯映照族.可以证明,这样的映照族本质上是由二个单复变数的全纯函数的直乘积所组成的族.本文证明:即使在Banach空间中,Cauchy-Riemann方程的全纯解,具有同样的性质. 相似文献
7.
Mats Andersson 《Bulletin des Sciences Mathématiques》2004,128(6):481-512
We define a residue current of a holomorphic mapping, or more generally of a holomorphic section of a holomorphic vector bundle, by means of Cauchy-Fantappie-Leray type formulas, and prove that a holomorphic function that annihilates this current belongs to the corresponding ideal locally. We also prove that the residue current coincides with the Coleff-Herrera current in the case of a complete intersection. The residue current is globally defined and this is used in some geometric applications. By means of the residue current we also construct, for an arbitrary ideal, an integral formula for interpolation and division. 相似文献
8.
We study a decomposition of a holomorphic vector bundle with connection which need not be endowed with any metrics, which is a generalization of an orthogonal decomposition of a Hermitian holomorphic vector bundle. We first derive several results on the induced connections, the second fundamental forms of subbundles and curvature forms of the connections. We next apply these results to a complex affine immersion. Especially, we give elementary self-contained proofs of the fundamental theorems for a complex affine immersion to a complex affine space. 相似文献
9.
John Ryan 《Journal of Functional Analysis》1987,70(2)
A number of Runge approximation theorems are proved for complex Clifford algebra valued holomorphic functions which either satisfy the holomorphic, homogeneous Dirac equation, or complex Laplacian. The results are applied to establish analogues of the homological version of the Mittag-Leffler theorem. 相似文献
10.
Joan Girbau 《Israel Journal of Mathematics》1981,40(3-4):235-254
In this paper we deal with a complex analytic foliation of a compact complex manifold endowed with a bundle-like metric and
give a transversally holomorphic rigidity theorem (Theorem 9.1) for these foliations, depending on curvature conditions. We
give some examples for which we study holomorphic rigidity. The classical vanishing theorems of Nakano, Griffiths and Le Potier
are the main tools we use to prove our results. 相似文献
11.
We first study the asymptotic behavior of nonlinear semigroups with holomorphic generators, and then use our results, inter alia, to construct holomorphic retractions onto the fixed point sets of holomorphic self-mappings of bounded convex domains in a complex Banach space. 相似文献
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Ngaiming Mok 《中国科学A辑(英文版)》2005,48(Z1)
We study holomorphic immersions f: X → M from a complex manifold X into a Kahler manifold of constant holomorphic sectional curvature M, i.e. a complex hyperbolic space form, a complex Euclidean space form, or the complex projective space equipped with the Fubini-Study metric. For X compact we show that the tangent sequence splits holomorphically if and only if f is a totally geodesic immersion. For X not necessarily compact we relate an intrinsic cohomological invariant p(X) on X, viz. the invariant defined by Gunning measuring the obstruction to the existence of holomorphic projective connections, to an extrinsic cohomological invariant v(f)measuring the obstruction to the holomorphic splitting of the tangent sequence. The two invariants p(X) and v(f) are related by a linear map on cohomology groups induced by the second fundamental form.In some cases, especially when X is a complex surface and M is of complex dimension 4, under the assumption that X admits a holomorphic projective connection we obtain a sufficient condition for the holomorphic splitting of the tangent sequence in terms of the second fundamental form. 相似文献
13.
Indranil Biswas 《代数通讯》2020,48(4):1452-1475
AbstractWe investigate relative connections on a sheaf of modules. A sufficient condition is given for the existence of a relative holomorphic connection on a holomorphic vector bundle over a complex analytic family. We show that the relative Chern classes of a holomorphic vector bundle admitting relative holomorphic connection vanish, if each of the fiber of the complex analytic family is compact and Kähler. 相似文献
14.
Roman J. Dwilewicz 《Monatshefte für Mathematik》2013,169(2):145-160
In this paper we give a complete characterization of vector bundles of any dimension over complex tori in which the Hartogs–Bochner holomorphic extension phenomenon holds. Since holomorphic sections of line bundles over complex tori can be identified with theta functions, the results are formulated in terms of this class. 相似文献
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In this paper we extend the results on projective changes of complex Finsler metrics obtained in Aldea and Munteanu (2012) [3], by the study of projective curvature invariants of a complex Finsler space. By means of these invariants, the notion of complex Douglas space is then defined. A special approach is devoted to the obtaining of equivalence conditions for a complex Finsler space to be a Douglas one. It is shown that any weakly Kähler Douglas space is a complex Berwald space. A projective curvature invariant of Weyl type characterizes complex Berwald spaces. These must be either purely Hermitian of constant holomorphic curvature, or non-purely Hermitian of vanishing holomorphic curvature. Locally projectively flat complex Finsler metrics are also studied. 相似文献
16.
Hartogs’ theorem asserts that a separately holomorphic function, defined on an open subset of
$$\mathbb {C}^n$$
, is holomorphic in all the variables. We prove a global variant of this theorem for functions defined on an open subset of the product of complex algebraic manifolds. We also obtain global Hartogs-type theorems for complex Nash functions and complex regular functions. 相似文献
17.
《Nonlinear Analysis: Real World Applications》2007,8(4):1132-1143
In [G. Munteanu, Complex Spaces in Finsler, Lagrange and Hamilton Geometries, vol. 141, Kluwer Academic Publishers, Dordrecht, FTPH, 2004.] we underlined the motifs of a remarkable class of complex Finsler subspaces, namely the holomorphic subspaces. With respect to the Chern–Finsler complex connection (see [M. Abate, G. Patrizio, Finsler Metrics—A Global Approach, Lecture Notes in Mathematics, vol. 1591, Springer, Berlin, 1994.]) we studied in [G. Munteanu, The equations of a holomorphic subspace in a complex Finsler space, Publicationes Math. Debrecen, submitted for publication.] the Gauss, Codazzi and Ricci equations of a holomorphic subspace, the aim being to determine the interrelation between the holomorphic sectional curvature of the Chern–Finsler connection and that of its induced tangent connection.In the present paper, by means of the complex Berwald connection, we study totally geodesic holomorphic subspaces. With respect to complex Berwald connection the equations of the holomorphic subspace have simplified expressions. The totally geodesic subspace request is characterized by using the second fundamental form of complex Berwald connection. 相似文献
18.
The authors introduce a new idea related to Montel-type theorems in higher dimension and prove some Montel-type criteria for normal families of holomorphic mappings and normal holomorphic mappings of several complex variables into p^N (C) for continuously moving hyperplanes in pointwise general position. The main results are also true for continuously moving hypersurfaces in pointwise general position. Examples are given to show the sharpness of the results. 相似文献
19.
本文对复变数几何函数论的结果向多复变函数的推广进行了系统的研究,是作者及其合作者们在此项研究工作上的一些成果的综合报导。此文集中讨论了有界对称域及Reinhardt域的情形,讨论了全纯映照为星形、凸及双全纯的种种条件,建立了一些双全纯映照族的偏差定理,增长定理及掩盖定理,定义了高维空间上的Schwartz导数。对有界对称域上的全纯凸函数的Bloch常数进行了估计,处理这些问题的主要工具之一为李代数 相似文献
20.
A new theory of regular functions over the skew field of Hamilton numbers (quaternions) and in the division algebra of Cayley numbers (octonions) has been recently introduced by Gentili and Struppa (Adv. Math. 216 (2007) 279–301). For these functions, among several basic results, the analogue of the classical Schwarz' Lemma has been already obtained. In this paper, following an interesting approach adopted by Burns and Krantz in the holomorphic setting, we prove some boundary versions of the Schwarz' Lemma and Cartan's Uniqueness Theorem for regular functions. We are also able to extend to the case of regular functions most of the related “rigidity” results known for holomorphic functions. 相似文献