共查询到20条相似文献,搜索用时 15 毫秒
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In this paper, we present the general analytic solution to the zero curvature equation for rigid three-dimensional CR-manifolds. The solutions are uniquely determined by one function and four real parameters. 相似文献
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A. V. Isaev 《Journal of Geometric Analysis》2008,18(3):795-799
We prove a characterization theorem for the unit polydisc Δ
n
⊂ℂ
n
in the spirit of a recent result due to Kodama and Shimizu. We show that if M is a connected n-dimensional complex manifold such that (i) the group Aut (M) of holomorphic automorphisms of M acts on M with compact isotropy subgroups, and (ii) Aut (M) and Aut (Δ
n
) are isomorphic as topological groups equipped with the compact-open topology, then M is holomorphically equivalent to Δ
n
.
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J. Heber 《Geometric And Functional Analysis》2006,16(4):869-890
We classify noncompact homogeneous spaces which are Einstein and asymptotically harmonic. This completes the classification of Riemannian harmonic spaces in the homogeneous case: Any simply connected homogeneous harmonic space is flat, or rank-one symmetric, or a nonsymmetric
Damek–Ricci space. Independently, Y. Nikolayevsky has obtained the latter classification under the additional assumption of
nonpositive sectional curvatures [N2].
Supported in part by DFG priority program “Global Differential Geometry” (SPP 1154).
Received: September 2004; Revision: June 2005; Accepted: September 2005 相似文献
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In this paper we study three dimensional homogeneous Finsler manifolds. We first obtain a complete list of the three‐dimensional homogeneous manifolds which admit invariant Finsler metrics. Then we consider invariant Randers metrics and present the classification of three dimensional homogeneous Randers spaces under isometrics. 相似文献
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We will prove that the automorphism groups of the strongly pseudoconvex model domains in almost complex manifolds are isomorphically embedded into the automorphism group of the unit ball. 相似文献
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Lens spaces are a family of manifolds that have been a source of many interesting phenomena in topology and differential geometry. Their concrete construction, as quotients of odd-dimensional spheres by a free linear action of a finite cyclic group, allows a deeper analysis of their structure. In this paper, we consider the problem of moments for the distance function between randomly selected pairs of points on homogeneous three-dimensional lens spaces. We give a derivation of a recursion relation for the moments, a formula for the kth moment, and a formula for the moment generating function, as well as an explicit formula for the volume of balls of all radii in these lens spaces. 相似文献
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Susana Coré 《Journal of Mathematical Analysis and Applications》2010,370(2):472-485
Let G be a homogeneous group with homogeneous dimension Q, and let So denote the space of Schwartz functions on G with all moments vanishing. Let be the usual Euclidean Fourier transform. For j∈R, we let be the space of J, smooth away from 0, satisfying |α∂J(ξ)|?Cβ|ξ|j−|β|, where both |ξ| and |β| are taken in the homogeneous sense. We characterize , and show that as elements of . If j1,j2,j1+j2>−Q, one can replace So, by S, S′ in this result. A key ingredient of our proof is a lemma from the fundamental wavelet paper from 1985 by Frazier and Jawerth [4]. We believe that, in turn, our result will be useful in the theory of wavelets on homogeneous groups. 相似文献
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Dmitri Alekseevsky Andreas Arvanitoyeorgos 《Transactions of the American Mathematical Society》2007,359(8):3769-3789
A geodesic in a Riemannian homogeneous manifold is called a homogeneous geodesic if it is an orbit of a one-parameter subgroup of the Lie group . We investigate -invariant metrics with homogeneous geodesics (i.e., such that all geodesics are homogeneous) when is a flag manifold, that is, an adjoint orbit of a compact semisimple Lie group . We use an important invariant of a flag manifold , its -root system, to give a simple necessary condition that admits a non-standard -invariant metric with homogeneous geodesics. Hence, the problem reduces substantially to the study of a short list of prospective flag manifolds. A common feature of these spaces is that their isotropy representation has two irreducible components. We prove that among all flag manifolds of a simple Lie group , only the manifold of complex structures in , and the complex projective space admit a non-naturally reductive invariant metric with homogeneous geodesics. In all other cases the only -invariant metric with homogeneous geodesics is the metric which is homothetic to the standard metric (i.e., the metric associated to the negative of the Killing form of the Lie algebra of ). According to F. Podestà and G.Thorbergsson (2003), these manifolds are the only non-Hermitian symmetric flag manifolds with coisotropic action of the stabilizer.
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In this paper, we consider the action of (2, q) on the finite projective line for q ≡ 1 (mod 4) and construct several infinite families of simple 3-designs which admit PSL(2, q) as an automorphism group. Some of the designs are also minimal. We also indicate a general outline to obtain some other
algebraic constructions of simple 3-designs.
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Andrea Spiro 《Proceedings of the American Mathematical Society》2000,128(4):1141-1145
Let be a compact homogeneous manifold with acting effectively and with a -invariant CR structure of hypersurface type; then any maximal compact subgroup acts transitively on .
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We show that ifM is the total space of a holomorphic bundle with base space a simply connected homogeneous projective variety and fibre and
structure group a compact complex torus, then the identity component of the automorphism group ofM acts trivially on the Dolbeault cohomology ofM. We consider a class of compact complex homogeneous spacesW, which we call generalized Hopf manifolds, which are diffeomorphic to S1 ×K/L whereK is a compact connected simple Lie group andL is the semisimple part of the centralizer of a one dimensional torus inK. We compute the Dolbeault cohomology ofW. We compute the Picard group of any generalized Hopf manifold and show that every line bundle over a generalized Hopf manifold
arises from a representation of its fundamental group. 相似文献
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Daniel Guan 《Transactions of the American Mathematical Society》2002,354(11):4493-4504
We solve the problem of the classification of compact complex homogeneous spaces with invariant volumes (see Matsushima, 1961).
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Wilhelm Kaup 《Archiv der Mathematik》2005,84(3):276-281
For certain classes of homogeneous Cauchy-Riemann manifolds it is shown that the local CR-equivalence problem is equivalent to the global CR-equivalence problem. Among these are large classes of compact linear group orbits.Received: 19 April 2004 相似文献
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