共查询到20条相似文献,搜索用时 15 毫秒
1.
Let $d_1,\,d_2$ , ... be a sequence of positive numbers that converges to zero. A generalization of Steinhaus’ theorem due to Weil implies that, if a subset of a homogeneous Riemannian manifold has no pair of points at distances $d_1,\,d_2$ , ... from each other, then it has to have measure zero. We present a quantitative version of this result for compact, connected, rank-one symmetric spaces, by showing how to choose distances so that the measure of a subset not containing pairs of points at these distances decays exponentially in the number of distances. 相似文献
2.
We extend the Gallot–Tanno theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over a manifold
admits a parallel symmetric (0, 2)-tensor then it is Riemannian. Applications of this result to the existence of metrics with
distinct Levi-Civita connections but having the same unparametrized geodesics and to the projective Obata conjecture are given.
We also apply our result to show that the holonomy group of a closed (O(p + 1, q), S
p,q
)-manifold does not preserve any nondegenerate splitting of
\mathbb Rp+1,q{\mathbb {R}^{p+1,q}}. 相似文献
3.
We prove the Cramér theorem forK-invariant Gaussian measures on irreducible symmetric spacesX=G/K withG semisimple noncompact. To do this we use a kind of Abel transform ofK-invariant measures onX.This research is supported by KBN Grant. 相似文献
4.
DENG Donggao & HAN Yongsheng Department of Mathematics Zhongshan University Guangzhou China Department of Mathematics Auburn University Alabama USA 《中国科学A辑(英文版)》2005,(5)
Using the discrete Calderon type reproducing formula and the Plancherel-Polya characterization for the Besov and Triebel-Lizorkin spaces, the T1 theorem for the Besov and Triebel-Lizorkin spaces was proved. 相似文献
5.
In this paper, as a first step to study the global structure of solution, we treat a class of reaction–diffusion systems with competitive interaction, and discuss a uniqueness theorem of radially symmetric solutions for the system. To do this, the comparison principle and the shooting method are employed, and the spatial profile is investigated. 相似文献
6.
Ján Špakula 《Archiv der Mathematik》2010,95(2):171-178
We prove a “quantified” version of the Weyl–von Neumann theorem, more precisely, we estimate the ranks of approximants to
compact operators appearing in Voiculescu’s theorem applied to commutative algebras. This allows considerable simplifications
in uniform K-homology theory, namely it shows that one can represent all the uniform K-homology classes on a fixed Hilbert space with a fixed *-representation of C
0(X), for a large class of spaces X. 相似文献
7.
We prove that compact quaternionic-Kähler manifolds of positive scalar curvature admit no almost complex structure, even in the weak sense, except for the complex Grassmannians Gr2(?n+2). We also prove that irreducible inner symmetric spaces M 4n of compact type are not weakly complex, except for spheres and Hermitian symmetric spaces. 相似文献
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SU Guang Xiang 《中国科学 数学(英文版)》2015,(2):423-446
In this paper,we extend Su-Zhang’s Cheeger-Mller type theorem for symmetric bilinear torsions to manifolds with boundary in the case that the Riemannian metric and the non-degenerate symmetric bilinear form are of product structure near the boundary.Our result also extends Brning-Ma’s Cheeger-Mller type theorem for Ray-Singer metric on manifolds with boundary to symmetric bilinear torsions in product case.We also compare it with the Ray-Singer analytic torsion on manifolds with boundary. 相似文献
10.
Felipe Leitner 《Mathematische Zeitschrift》2007,256(2):443-459
We describe and construct pseudo-Hermitian structures θ without torsion (i.e. with transverse symmetry) whose Webster–Ricci curvature tensor is a constant multiple of the exterior differential dθ. We call these structures TS-pseudo-Einstein and our first result states that all these structures can locally be derived from Kähler–Einstein metrics. Then we discuss the corresponding Fefferman metrics of the TS-pseudo-Einstein structures. These are never Einstein. However, our second result states that they are locally always conformally Einstein. 相似文献
11.
In this paper, we study strongly convex Kähler–Finsler manifolds. We prove two theorems: A strongly convex Kähler–Berwald manifold with a pole is a Stein manifold if it has nonpositive horizontal radial flag curvature; A strongly convex Kähler–Finsler manifold with a complex pole is a Stein manifold if it has nonpositive horizontal radial flag curvature. 相似文献
12.
Soji Kaneyuki 《中国科学A辑(英文版)》2005,48(Z1)
Symmetric spaces of Cayley type are a higher dimensional analogue of a one-sheeted hyperboloid in R3. They form an important class of causal symmetric spaces. To a symmetric space of Cayley type M, one can associate a bounded symmetric domain of tube type D. We determine the full causal automorphism group of M. This clarifies the relation between the causal automorphism group and the holomorphic automorphism group of D. 相似文献
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14.
Further investigation is done on a phenomenon studied by Zamfirescu in finite dimensions. Among other results it is proved that for most closed bounded sets A in a separable Banach space Y and most ${u \in A}$ , the union of all rays from u that meet A\{u} (resp. do not meet A\{u}) is dense in Y. An infinite-dimensional extension of a theorem of Wieacker is obtained, viz most compacta in a separable Banach space have smooth closed convex hulls. 相似文献
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Let ? be the genealogical tree of a supercritical multitype Galton–Watson process, and let Λ be the limit set of ?, i.e., the set of all infinite self-avoiding paths (called ends) through ? that begin at a vertex of the first generation. The limit set Λ is endowed with the metric d(ζ, ξ) = 2
−n
where n = n(ζ, ξ) is the index of the first generation where ζ and ξ differ. To each end ζ is associated the infinite sequence Φ(ζ) of
types of the vertices of ζ. Let Ω be the space of all such sequences. For any ergodic, shift-invariant probability measure
μ on Ω, define Ωμ to be the set of all μ-generic sequences, i.e., the set of all sequences ω such that each finite sequence v occurs in ω with limiting frequency μ(Ω(v)), where Ω(v) is the set of all ω′?Ω that begin with the word v. Then the Hausdorff dimension of Λ∩Φ−1 (Ωμ) in the metric d is
almost surely on the event of nonextinction, where h(μ) is the entropy of the measure μ and q(i, j) is the mean number of type-j offspring of a type-i individual. This extends a theorem of HAWKES [5], which shows that the Hausdorff dimension of the entire boundary at infinity is log2 α, where α is the Malthusian parameter.
Received: 30 June 1998 / Revised: 4 February 1999 相似文献
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A complex Radon measure μ on ℝ
n
is said to be of at most exponential-quadratic growth if there exist positive constants C and α such that
. Let Xexp denote the space of all complex Radon measure on ℝ
n
of at most exponential-quadratic growth. Using elementary methods, we obtain injectivity sets for spherical means for Xexp. We also discuss similar results for symmetric spaces. 相似文献