共查询到20条相似文献,搜索用时 140 毫秒
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本文讨论多重调和映射的等周型和Fejer-Riesz型不等式.首先,本文改进Kalaj和Meˇstrovi′c的相应结果,并将其结果推广到多重调和映射.其次,本文证明Pavlovi′c和Dostani′c的相应结果对于多重调和映射也是成立的.最后,本文建立关于多重调和映射的Fejer-Riesz型不等式. 相似文献
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本文讨论从曲面到复Grassmann流形Gk,N中的调和映射,给出了调和序列中的基本直射变换与因子分解中的基本旗变换的关系,从而证明了有阶的调和映射与有限的调和映射是一致的. 相似文献
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构造了到CPn的非全实Lagrange调和映射的例子,刻划了从Riemann面到CPn的调和映射其象空间含于RPn的特征. 相似文献
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研究多重调和Bergman空间上的Topelitz算子.对多重调和符号的Topelitz算子,给出了乘积性质、交换性质的符号描述. 相似文献
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焦晓祥 《数学年刊A辑(中文版)》2000,(1)
本文讨论从曲面到复Grassmann流形Gk,N中的调和映射,给出了调和序列中的基本直射变换与 因子分解中的基本旗变换的关系,从而证明了有阶的调和映射与有限的调和映射是一致的. 相似文献
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周春琴 《高校应用数学学报(A辑)》2002,17(3):323-328
讨论一类映入球面的满足拟单调不等式的弱调和映射的边界正则性。利用函数的延拓技巧以及Hardy空间和BMO空间的对偶性,对这类弱调和映射的边界正则性给出一个简明的证明。 相似文献
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分别考虑了映入球面及紧致的齐性Riemannian空间的弱P-调和映射流;通过球面及齐性Riemannian空间的对称性质,证明了弱P-调和映射流的紧性性质. 相似文献
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本文给出了从具有正第一陈类的紧Kaehler流形到四元射影空间的多重调和映照的完全分类. 相似文献
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Curved flats,pluriharmonic maps and constant curvature immersions into pseudo-Riemannian space forms 总被引:1,自引:0,他引:1
David Brander 《Annals of Global Analysis and Geometry》2007,32(3):253-275
We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first
aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various equivalences
between global isometric immersion problems among different space forms and pseudo-Riemannian space forms. As a corollary,
we obtain a non-immersibility theorem for spheres into certain pseudo-Riemannian spheres and hyperbolic spaces. The second
aspect pursued is to clarify the relationship between the loop group formulation of isometric immersions of space forms and
that of pluriharmonic maps into symmetric spaces. We show that the objects in the first class are, in the real analytic case,
extended pluriharmonic maps into certain symmetric spaces which satisfy an extra reality condition along a totally real submanifold.
We show how to construct such pluriharmonic maps for general symmetric spaces from curved flats, using a generalised DPW method.
相似文献
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Like minimal surface immersions in 3-space, pluriharmonic maps into symmetric spaces allow a one-parameter family of isometric deformations rotating the differential (“associated family”); in fact, pluriharmonic maps are characterized by this property. We give a geometric proof of this fact and investigate the “isotropic” case where this family is constant. It turns out that isotropic pluriharmonic maps arise from certain holomorphic maps into flag manifolds. Further, we also consider higher dimensional generalizations of constant mean curvature surfaces which are Kähler submanifolds with parallel (1,1) part of their soecond fundamental form; under certain restrictions there are also characterized by having some kind of (“weak”) associated family. Examples where this family is constant arise from extrinsic Kähler symmetric spaces. 相似文献
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Like minimal surface immersions in 3-space, pluriharmonic maps into symmetric spaces allow a one-parameter family of isometric
deformations rotating the differential (“associated family”); in fact, pluriharmonic maps are characterized by this property.
We give a geometric proof of this fact and investigate the “isotropic” case where this family is constant. It turns out that
isotropic pluriharmonic maps arise from certain holomorphic maps into flag manifolds. Further, we also consider higher dimensional
generalizations of constant mean curvature surfaces which are K?hler submanifolds with parallel (1,1) part of their soecond
fundamental form; under certain restrictions there are also characterized by having some kind of (“weak”) associated family.
Examples where this family is constant arise from extrinsic K?hler symmetric spaces.
Received: 8 July 1997 相似文献
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ONFACTORIZATIONTHEOREMSOFPLURIHARMONICMAPSINTOTHEUNITARYGROUPCHENGQIYUANDONGYUXINabstractTheauthorsgivesomeconstructive... 相似文献
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We show that given a harmonic map φ from a Riemann surface to a classical compact simply connected inner symmetric space, there is a J 2-holomorphic twistor lift of φ (or its negative) if and only if it is nilconformal. In the case of harmonic maps of finite uniton number, we give algebraic formulae in terms of holomorphic data which describes their extended solutions. In particular, this gives explicit formulae for the twistor lifts of all harmonic maps of finite uniton number from a surface to the above symmetric spaces. 相似文献
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In this paper, we show that one can interrelate pluriharmonic maps with para-pluriharmonic maps by means of the loop group method. As an appendix, we give examples for the interrelation between pluriharmonic maps and para-pluriharmonic maps. Moreover, we investigate the relation among CMC-surfaces by use of such maps. 相似文献
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《数学物理学报(B辑英文版)》2020,(1)
In this article, we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables. Surprisingly, the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same. Also, some interesting symmetry properties of complex symmetric Toeplitz operators are obtained. 相似文献
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Georgios Daskalopoulos Chikako Mese Alina Vdovina 《Geometric And Functional Analysis》2011,21(4):905-919
In this paper, we study the behavior of harmonic maps into complexes with branching differentiable manifold structure. The
main examples of such target spaces are Euclidean and hyperbolic buildings. We show that a harmonic map from an irreducible
symmetric space of noncompact type other than real or complex hyperbolic into these complexes are non-branching. As an application,
we prove rank-one and higher-rank superrigidity for the isometry groups of a class of complexes which includes hyperbolic
buildings as a special case. 相似文献
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Twistors, 4-symmetric spaces and integrable systems 总被引:1,自引:0,他引:1
An order four automorphism of a Lie algebra gives rise to an integrable system introduced by Terng. We show that solutions
of this system may be identified with certain vertically harmonic twistor lifts of conformal maps of surfaces in a Riemannian
symmetric space. As applications, we find that surfaces with holomorphic mean curvature in 4-dimensional real or complex space
forms constitute an integrable system as do Hamiltonian stationary Lagrangian surfaces in 4-dimensional Hermitian symmetric
spaces (this last providing a conceptual explanation of a result of Hélein-Romon). 相似文献