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1.
The aim of this paper is to present some results about spin structures on flat manifolds. We prove that any finite group can
be the holonomy group of a flat spin manifold. Moreover, we shall give some methods of constructing spin structures related
to the holonomy representation. 相似文献
2.
We study spin structures on flat Riemannian manifolds. The main result is a necessary and sufficient condition for a flat manifold with cyclic holonomy to have a spin structure. 相似文献
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V. S. Kal'nitskii 《Journal of Mathematical Sciences》2005,131(1):5345-5350
A classification theorem for the Jacobi algebras on flat manifolds is proved.The proof involves a generalization of a result
about the Lie algebra
n(ℝ). Bibliography: 8 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 152–161. 相似文献
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R. MIRZAIE 《数学学报(英文版)》2007,23(9):1587-1592
In this paper, we study flat Riemannian manifolds which have codimension two orbits, under the action of a closed and connected Lie group G of isometries. We assume that G has fixed points, then characterize M and orbits of M. 相似文献
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Andrzej Szczepański 《Geometriae Dedicata》2006,120(1):111-118
We present about twenty conjectures, problems and questions about flat manifolds. Many of them build the bridges between the flat world and representation theory of the finite groups, hyperbolic geometry and dynamical systems.
In memory of Charles B. Thomas 相似文献
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F. Ö. Zengin 《Ukrainian Mathematical Journal》2014,65(11):1725-1732
10.
Paola Matzeu 《Monatshefte für Mathematik》2002,136(4):297-311
We consider compact Weyl submanifolds of Weyl flat manifolds with special attention on compact Einstein-Weyl hypersurfaces.
In particular, in the last part of the paper, we study Weyl submanifolds of special noncompact manifolds, called PC-manifolds.
Received July 16, 2001; in revised form February 6, 2002 Published online August 9, 2002 相似文献
11.
Paola Matzeu 《Monatshefte für Mathematik》2002,13(5):297-311
We consider compact Weyl submanifolds of Weyl flat manifolds with special attention on compact Einstein-Weyl hypersurfaces.
In particular, in the last part of the paper, we study Weyl submanifolds of special noncompact manifolds, called PC-manifolds. 相似文献
12.
We describe up to finite coverings causal flat affine complete Lorentzian manifolds such that the past and the future of any
point are closed near this point. We say that these manifolds are strictly causal. In particular, we prove that their fundamental
groups are virtually abelian. In dimension 4, there is only one, up to a scaling factor, strictly causal manifold which is
not globally hyperbolic. For a generic point of this manifold, either the past or the future is not closed and contains a
lightlike straight line 相似文献
13.
Tomasz Filar 《代数通讯》2013,41(6):2380-2387
Vasquez showed that for any finite group G there exists a number n(G) such that for every flat Riemannian manifold M with holonomy group G there exists a fiber bundle T → M → N, where T is a flat torus and N is a flat manifold of dimension less than or equal to n(G). We show that n(H) ≤ n(G) if H Δ leftG or G = N ? H and use this result to describe groups with the Vasquez number equal to 2 or 3. 相似文献
14.
Following in the tradition of Hilbert's 18th problem of classifying crystallographic groups, we provide a survey of a series of results which have culminated in the study of flat Lorentz manifolds. In particular, Milnor asked whether all complete flat affine manifolds have virtually polycyclic fundamental groups. Margulis answered this question negatively by constructing complete flat Lorentz manifolds with free fundamental groups. In this paper, we follow the effort to classify and understand these interesting counterexamples to Milnor's question, and their generalizations. 相似文献
15.
Roberto Tauraso 《Monatshefte für Mathematik》1999,120(1):151-157
It is proven that the sets of periods for expanding maps on n-dimensional flat manifolds are uniformly cofinite, i.e. there is a positive integer m 0, which depends only on n, such that for any integer , for any n-dimensional flat manifold ℳ and for any expanding map F on ℳ, there exists a periodic point of F whose least period is exactly m. 相似文献
16.
Roberto Tauraso 《Monatshefte für Mathematik》1999,128(2):151-157
It is proven that the sets of periods for expanding maps on n-dimensional flat manifolds are uniformly cofinite, i.e. there is a positive integer m
0, which depends only on n, such that for any integer , for any n-dimensional flat manifold ℳ and for any expanding map F on ℳ, there exists a periodic point of F whose least period is exactly m.
(Received 10 April 1998; in revised form 20 January 1999) 相似文献
17.
§1. IntroductionLetMbeann-dimensionalconformallyflatmanifoldwithconstantscalarcurvatureρ(n≥3).WhentheRiccicurvatureSofMisofboundedbelowandySy2<ρ2/(n-1),Gold-bergprovedthatMisofconstantcurvature[1].WhenMisacompactmanifoldwithpositiveRiccicurvature,WuB… 相似文献
18.
We describe the possible holonomy groups of simply connected irreducible non-locally symmetric pseudo-Riemannian spin manifolds which admit parallel spinors. 相似文献
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Changpeng PAN 《数学年刊B辑(英文版)》2021,42(4):575-582
In this paper, the author solves the Dirichlet problem for Hermitian-Poisson metric equation √?1ΛωGH = λId and proves the existence of Hermitian-Poisson metrics on flat bundles over a class of complete Hermitian manifolds. When λ = 0, the HermitianPoisson metric is a Hermitian harmonic metric. 相似文献