共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper contains a proof of the following property of compact irreducible Hermitian symmetric spaces. If H=G/K where G is a compact simply connected simple Lie group, T a maximal torus of G and F(T,H)=|E
1,...,E
m is the fixed point set of T on H, then for each pair E
i
, E
j
there is a 2-dimentional sphere N
ij
H such that E
i and E
j are antipodal points of N
ij. 相似文献
2.
A. I. Shtern 《Mathematical Notes》2005,78(1-2):128-133
It is shown that an arbitrary irreducible continuous unitary projective representation of a simple Hermitian symmetric Lie group is generated by a strongly continuous pure unitary pseudorepresentation of the adjoint group of the Lie group.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 140–146.Original Russian Text Copyright © 2005 by A. I. Shtern. 相似文献
3.
Genkai Zhang 《Acta Appl Math》2002,73(1-2):79-94
We give a brief survey on the study of constructions of invariant differential operators on Riemannian symmetric spaces and of combinatorial and analytical properties of their eigenvalues, and pose some open questions. 相似文献
4.
WeiYueDING HongYuWANG YouDeWANG 《数学学报(英文版)》2003,19(2):303-312
In this note,we prove that the Schroedinger flow of maps from a closed riemann surface into a compact irreducible Hermitian symmetic space admits a global weak solution.Also,we show the existence of weak solutions to the initial value problem of Heisenberg model with Lie algebra values,which is closely related to the Schroedinger flow on compact Hermitian symmetric spaces. 相似文献
5.
Let \(M := \Gamma\backslash G/K\) be the quotient of an irreducible Hermitian symmetric space G/K by a torsionfree cocompact lattice \(\Gamma\subset G\) . There is a natural flat principal G-bundle over the compact Kähler manifold M which is constructed from the principal Γ-bundle over M defined by the quotient map \(G/K\longrightarrow M\) . We construct the principal G-Higgs bundle over M corresponding to this flat G-bundle. This principal G-Higgs bundle is rigid if \({\rm dim}_\mathbb{C} M\,\geq\,2\) . 相似文献
6.
The Hermitian tensor is an extension of Hermitian matrices and plays an important role in quantum information research. It is known that every symmetric tensor has a symmetric CP-decomposition. However, symmetric Hermitian tensor is not the case. In this paper, we obtain a necessary and sufficient condition for symmetric Hermitian decomposability of symmetric Hermitian tensors. When a symmetric Hermitian decomposable tensor space is regarded as a linear space over the real number field, we also obtain its dimension formula and basis. Moreover, if the tensor is symmetric Hermitian decomposable, then the symmetric Hermitian decomposition can be obtained by using the symmetric Hermitian basis. In the application of quantum information, the symmetric Hermitian decomposability condition can be used to determine the symmetry separability of symmetric quantum mixed states. 相似文献
7.
An infinite family of minimal blocking sets of ??(3, q2) is constructed for even q, with links to Ceva configurations. Copyright © 2011 John Wiley & Sons, Ltd 19:313‐316, 2011. 相似文献
8.
Ngaiming MOK 《数学年刊B辑(英文版)》2008,29(2):135-146
The author,motivated by his results on Hermitian metric rigidity,conjectured in [4] that a proper holomorphic mapping f:Ω→Ω′from an irreducible bounded symmetric domainΩof rank≥2 into a bounded symmetric domainΩ′is necessarily totally geodesic provided that r′:=rank(Ω′)≤rank(Ω):=r.The Conjecture was resolved in the affirmative by I.-H.Tsai [8].When the hypothesis r′≤r is removed,the structure of proper holomorphic maps f:Ω→Ω′is far from being understood,and the complexity in studying such maps depends very much on the difference r′-r,which is called the rank defect.The only known nontrivial non-equidimensional structure theorems on proper holomorphic maps are due to Z.-H.Tu [10],in which a rigidity theorem was proven for certain pairs of classical domains of type I,which implies nonexistence theorems for other pairs of such domains.For both results the rank defect is equal to 1,and a generaliza- tion of the rigidity result to cases of higher rank defects along the line of arguments of [10] has so far been inaccessible. In this article, the author produces nonexistence results for infinite series of pairs of (Ω→Ω′) of irreducible bounded symmetric domains of type I in which the rank defect is an arbitrarily prescribed positive integer. Such nonexistence results are obtained by exploiting the geometry of characteristic symmetric subspaces as introduced by N. Mok and L-H Tsai [6] and more generally invariantly geodesic subspaces as formalized in [8]. Our nonexistence results motivate the formulation of questions on proper holomorphic maps in the non-equirank case. 相似文献
9.
Leonardo Biliotti 《Transactions of the American Mathematical Society》2006,358(7):3003-3022
We obtain the full classification of coisotropic and polar isometric actions of compact Lie groups on irreducible Hermitian symmetric spaces.
10.
Luis Hernández-lamoneda 《Geometriae Dedicata》2000,79(2):205-218
A Bochner-type formula for almost Hermitian manifolds is introduced. From this formula, one can find obstructions imposed by the curvature to the existence of certain almost Hermitian structures on compact manifolds. 相似文献
11.
We generalize the Ashtekar–Isham construction for quantizing gauge fields to the case where the configuration variables belong to the space of Hermitian triples, not Hermitian connections. 相似文献
12.
Huafei Sun 《Geometriae Dedicata》2002,90(1):63-75
We study minimal submanifolds in the locally symmetric and conformally flat Riemannian manifold and generalize Yau's result obtained in J. Amer. Math. 97 (1975), 76–100. 相似文献
13.
14.
15.
Roberto Mossa 《Differential Geometry and its Applications》2013,31(5):594-601
We calculate the volume entropy of local Hermitian symmetric spaces of noncompact type in terms of its invariant r, a, b. 相似文献
16.
Let Г be a torsion-free uniform lattice of SU(m, 1), m > 1. Let G be either SU(p, 2) with p ≥ 2, ${{\rm Sp}(2,\mathbb {R})}Let Г be a torsion-free uniform lattice of SU(m, 1), m > 1. Let G be either SU(p, 2) with p ≥ 2, or SO(p, 2) with p ≥ 3. The symmetric spaces associated to these G’s are the classical bounded symmetric domains of rank 2, with the exceptions of SO*(8)/U(4) and SO*(10)/U(5). Using the correspondence
between representations of fundamental groups of K?hler manifolds and Higgs bundles we study representations of the lattice
Г into G. We prove that the Toledo invariant associated to such a representation satisfies a Milnor-Wood type inequality and that
in case of equality necessarily G = SU(p, 2) with p ≥ 2m and the representation is reductive, faithful, discrete, and stabilizes a copy of complex hyperbolic space (of maximal possible
induced holomorphic sectional curvature) holomorphically and totally geodesically embedded in the Hermitian symmetric space
SU(p, 2)/S(U(p) × U(2)), on which it acts cocompactly. 相似文献
17.
Let 𝔤 be a finite-dimensional complex semisimple Lie algebra and σ an arbitrary semisimple automorphism of 𝔤. Let 𝔱 be a Cartan subalgebra of 𝔨 = 𝔤σ and 𝔥 =Z 𝔤(𝔱) be the centralizer of 𝔱 in 𝔤. Then 𝔥 is a σ-invariant Cartan subalgebra of 𝔤 and 𝔱 = 𝔥σ. Let W(𝔤, 𝔥) be the Weyl group. One knows that Δ(𝔤, 𝔱), the set of roots of 𝔤 in 𝔱, is also a root system. It is proved that the corresponding Weyl group W(𝔤, 𝔱) is isomorphic to W(𝔤, 𝔥)σ, which is the subgroup of W(𝔤, 𝔥) consisting of those elements commuting with σ. It is also shown that the image of the restriction map S(𝔥*) W(𝔤, 𝔥) → S(𝔱*) W(𝔨, 𝔱), where S(𝔥*) and S(𝔱*) are the polynomial algebras on 𝔥 and 𝔱, respectively, is exactly S(𝔱*) W(𝔤, 𝔱). Based on the above result, we also get a complete classification of the pairs (𝔤, σ) such that 𝔤σ is noncohomologous to zero in 𝔤. 相似文献
18.
Theodoros Vlachos 《Geometriae Dedicata》1997,68(1):73-78
We use the maximum principle for second-order elliptic operators to establish a sufficient condition for a compact hypersurface in a space form to be a geodesic sphere in terms of a pinching for the s-mean curvature. 相似文献
19.
§1. IntroductionTheheatkernelofamaniforldcontainsrichimformationofgeometryandanalysisofthemanifold.Recenty,manymathematiciansandphysistsareinterestedinthisfieldandalotofimportantresultsareobtained.LetPn(C)denotethesetofalln×ncomplexHermitepositivedef… 相似文献
20.
R. Quiroga-Barranco 《Geometriae Dedicata》1998,71(3):287-298
We show that the canonical isometric imbedding of the symplectic group Sp(n) into R4n2 gives the least-dimensional isometric imbedding into the Euclidean space, even in the local standpoint. We prove this result by calculating the quantity pG determined by the curvature of Sp(n), which serves as an obstruction to the existence of local isometric imbeddings. We also exhibit the estimates on the value pG for the remaining compact classical simple Lie groups, and improve the previous results on the codimension of local isometric imbeddings of these groups. 相似文献