共查询到20条相似文献,搜索用时 15 毫秒
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We consider holomorphic mappings sending a given Levi-nondegenerate pseudoconcave hypersurface M in Cn+1 into a nondegenerate hyperquadric of the same signature in PCN+1 and show that if M is sufficiently close to a hyperquadric in a certain sense, then any two such mappings differ only by an automorphism of the hyperquadric. 相似文献
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Kim (Arch Math (Basel) 79(3):208–215, 2002) constructs multilinear differential operators for Hermitian Jacobi forms and Hermitian modular forms. However, her work relies on incorrect actions of differential operators on spaces of Hermitian Jacobi forms and Hermitian modular forms. In particular, her results are incorrect if the underlying field is the Gaussian number field. We consider more general spaces of Hermitian Jacobi forms and Hermitian modular forms over \(\mathbb {Q}(i)\), which allow us to correct the corresponding results in Kim (2002). 相似文献
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Estimating upper bounds of the spectrum of large Hermitian matrices has long been a problem with both theoretical and practical significance. Algorithms that can compute tight upper bounds with minimum computational cost will have applications in a variety of areas. We present a practical algorithm that exploits k-step Lanczos iteration with a safeguard step. The k is generally very small, say 5-8, regardless of the large dimension of the matrices. This makes the Lanczos iteration economical. The safeguard step can be realized with marginal cost by utilizing the theoretical bounds developed in this paper. The bounds establish the theoretical validity of a previous bound estimator that has been successfully used in various applications. Moreover, we improve the bound estimator which can now provide tighter upper bounds with negligible additional cost. 相似文献
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We determine precisely for which spherical space forms there are nontrivial smooth CR mappings to spheres. Equivalently we determine for which fixed point free finite unitary groups ? there exists a ?-invariant proper holomorphic rational map between balls. The answer is that the group must be cyclic and essentially only two classes of representations can occur. For these there are invariant polynomial examples. 相似文献
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We show that conformal mappings between the Engel groups are CR or anti-CR mappings. This reduces the determination of conformal
mappings to a problem in the theory of several complex analysis. The result about the group of CR automorphisms is used to
determine the identity component of the group of conformal mappings on the Engel group. 相似文献
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We characterize irreducible Hermitian symmetric spaces which are not of tube type, both in terms of
the topology of the space of triples of pairwise transverse points in the Shilov boundary, and of two invariants which we
introduce, the Hermitian triple product and its complexification. We apply these results and the techniques introduced in
[6] to characterize conjugacy classes of Zariski dense representations of a locally compact group into the connected component
G of the isometry group of an irreducible Hermitian symmetric space which is not of tube type, in terms of the pullback of
the bounded Kahler class via the representation. We conclude also that if the second bounded cohomology of a finitely generated
group Γ is finite dimensional, then there are only finitely many conjugacy classes of representations of Γ into G with Zariski
dense image. This generalizes results of [6]. 相似文献
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Sloan Fellow, partially supported by NSF grant DMS 8619858 相似文献
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M. G. Mahmoudi 《manuscripta mathematica》2005,116(4):493-516
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Properties of Hermitian forms are used to investigate several natural questions from CR geometry. To each Hermitian symmetric
polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the polynomial
product. We show, except for three trivial cases, that every signature pair can be obtained from the product of two indefinite
forms. We provide several new applications to the complexity theory of rational mappings between hyperquadrics, including
a stability result about the existence of non-trivial rational mappings from a sphere to a hyperquadric with a given signature
pair. 相似文献
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The purpose of this article is to study Lipschitz CR mappings from an h-extendible (or semi-regular) hypersurface in ${\mathbb{C}^n}$ . Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A rigidity result for proper holomorphic mappings from strongly pseudoconvex domains is also proved. 相似文献
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M. D. Kovalev 《Journal of Mathematical Sciences》2008,149(1):947-955
The bounds of minimal rank of differentials of rigidity mappings are obtained. They depend on the structural scheme and on
the positions of fastened points. Two hypotheses are introduced. One on presence in the set of minimal rank of the rigidity
mapping of a construction with a zero-length lever. Another—on the unboundedness of the sets of constant rank of the rigidity
mapping in the case of their positive dimension. In some cases these hypotheses are proved. 相似文献
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The well-known Chowla and Zassenhaus conjecture, proven by Cohen in 1990, states that for any \(d\ge 2\) and any prime \(p>(d^2-3d+4)^2\) there is no complete mapping polynomial in \(\mathbb {F}_p[x]\) of degree d. For arbitrary finite fields \(\mathbb {F}_q\), we give a similar result in terms of the Carlitz rank of a permutation polynomial rather than its degree. We prove that if \(n<\lfloor q/2\rfloor \), then there is no complete mapping in \(\mathbb {F}_q[x]\) of Carlitz rank n of small linearity. We also determine how far permutation polynomials f of Carlitz rank \(n<\lfloor q/2\rfloor \) are from being complete, by studying value sets of \(f+x.\) We provide examples of complete mappings if \(n=\lfloor q/2\rfloor \), which shows that the above bound cannot be improved in general. 相似文献
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We consider the subgroup G(n) of the compact unitary group U(n) generated by reflections. By a reflection we mean an element R of U(n) such that R2=I and ?1 is a simple eigenvalue of R. It is easy to describe the relations between reflections of the form R1R2=R3R4. One of our main results is that these relations together with R2=I are the defining relations of G(n). Other results characterize the set of all shortest sequences R1, R2,…, Rm of reflections whose product is a fixed element of G(n). 相似文献
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Douglas W. Larmour 《Mathematische Zeitschrift》2006,252(3):459-472
Throughout this paper, we let (D,σ) be a central F -division algebra with involution σ such that Fσ={d ∈ F|σ(d)=d} is a Henselian valued field. By [11], the valuation on Fσ extends uniquely to a valuation on D. We denote this valuation by v. Moreover, we assume that the characteristic of the residue field, , is not 2. If the valuation on F is discrete, then any quadratic form q can be written as q= q1⊥πq2, where π is a uniformizer and qi are unit forms. Springer's Theorem states that q is isotropic if and only if at least one of the residue forms and is isotropic. In this paper we generalize this result to ɛ -Hermitian forms. In Section 4, we use the connection between involutions on algebras and ɛ-Hermitian forms to prove an analog of the Springer Theorem for involutions.
This paper was part of the author's doctoral dissertation at New Mexico State University. The author wishes to thank his advisor
Pat Morandi for his tireless help. 相似文献
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We prove a gap rigidity theorem for diagonal curves in maximal polyspheres of irreducible compact Hermitian symmetric spaces of tube type, which is a dual analog to a theorem obtained by Mok. Motivated by the proof we show that the Chow space of certain totally geodesic submanifolds is affine algebraic, which gives a weaker version of gap rigidity for a class of higher dimensional submanifolds. 相似文献