共查询到20条相似文献,搜索用时 651 毫秒
1.
Miguel Sánchez 《Differential Geometry and its Applications》2006,24(1):21-32
Some results related to the causality of compact Lorentzian manifolds are proven: (1) any compact Lorentzian manifold which admits a timelike conformal vector field is totally vicious, and (2) a compact Lorentzian manifold covered regularly by a globally hyperbolic spacetime admits a timelike closed geodesic, if some natural topological assumptions (fulfilled, for example, if one of the conjugacy classes of deck transformations containing a closed timelike curve is finite) hold. As a consequence, any compact Lorentzian manifold conformal to a static spacetime is geodesically connected by causal geodesics, and admits a timelike closed geodesic. 相似文献
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3.
For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of
the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose of
this construction is to realise the normal conformal Tractor holonomy as affine holonomy of such a connection. We give an
example of an ambient connection for which this is the case, and which is torsion free if we start the construction with a
C-space, and in addition Ricci-flat if we start with an Einstein manifold. Thus, for a C-space this example leads to an ambient metric in the weaker sense of Čap and Gover, and for an Einstein space to a Ricci-flat
ambient metric in the sense of Fefferman and Graham.
Current address for first author: Erwin Schr?dinger International Institute for Mathematical Physics (ESI), Boltzmanngasse
9, 1090 Vienna, Austria
Current address for second author: Department of Mathematics, University of Hamburg, Bundesstra?e 55, 20146 Hamburg, Germany 相似文献
4.
In this article, after giving a necessary and sufficient condition for two Einstein- Weyl manifolds to be in conformal correspondence, we prove that any conformal mapping between such manifolds is generalized concircular if and only if the covector field of the conformal mapping is locally a gradient. Using this fact we deduce that any conformal mapping between two isotropic Weyl manifolds is a generalized concircular mapping. Moreover, it is shown that a generalized concircularly flat Weyl manifold is generalized concircular to an Einstein manifold and that its scalar curvature is prolonged covariant constant. 相似文献
5.
In this article, after giving a necessary and sufficient condition for two Einstein-Weyl manifolds to be in conformal correspondence, we prove that any conformal mapping between such manifolds is generalized concircular if and only if the covector field of the conformal mapping is locally a gradient. Using this fact we deduce that any conformal mapping between two isotropic Weyl manifolds is a generalized concircular mapping. Moreover, it is shown that a generalized concircularly flat Weyl manifold is generalized concircular to an Einstein manifold and that its scalar curvature is prolonged covariant constant. 相似文献
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7.
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
8.
Graham Hall 《Central European Journal of Mathematics》2012,10(5):1763-1770
This paper discusses the connection between projective relatedness and conformal flatness for 4-dimensional manifolds admitting
a metric of signature (+,+,+,+) or (+,+,+,−). It is shown that if one of the manifolds is conformally flat and not of the
most general holonomy type for that signature then, in general, the connections of the manifolds involved are the same and
the second manifold is also conformally flat. Counterexamples are provided which place limitations on the potential strengthening
of the results. 相似文献
9.
Stuart Armstrong 《Annals of Global Analysis and Geometry》2008,33(2):137-160
The aim of this paper and its prequel is to introduce and classify the irreducible holonomy algebras of the projective Tractor
connection. This is achieved through the construction of a ‘projective cone’, a Ricci-flat manifold one dimension higher whose
affine holonomy is equal to the Tractor holonomy of the underlying manifold. This paper uses the result to enable the construction
of manifolds with each possible holonomy algebra. 相似文献
10.
In this paper, conformal Kenmotsu manifolds are introduced. We consider CR-hypersurfaces of a conformal Kenmotsu manifold whose shape operator is parallel, scalar, recurrent or Lie \( \xi \)-parallel. It is proved that if the Lee vector field of a conformal Kenmotsu manifold is tangent and normal to these type of CR-hypersurfaces then the CR-hypersurfaces are totally geodesic and totally umbilic, respectively. An example of a three-dimensional conformal Kenmotsu manifold is constructed for illustration that is not Kenmotsu. 相似文献
11.
Cs. Vincze 《Differential Geometry and its Applications》2006,24(1):1-20
As it is well-known, a Minkowski space is a finite dimensional real vector space equipped with a Minkowski functional F. By the help of its second order partial derivatives we can introduce a Riemannian metric on the vector space and the indicatrix hypersurface S:=F−1(1) can be investigated as a Riemannian submanifold in the usual sense.Our aim is to study affine vector fields on the vector space which are, at the same time, affine with respect to the Funk metric associated with the indicatrix hypersurface. We give an upper bound for the dimension of their (real) Lie algebra and it is proved that equality holds if and only if the Minkowski space is Euclidean. Criteria of the existence is also given in lower dimensional cases. Note that in case of a Euclidean vector space the Funk metric reduces to the standard Cayley-Klein metric perturbed with a nonzero 1-form.As an application of our results we present the general solution of Matsumoto's problem on conformal equivalent Berwald and locally Minkowski manifolds. The reasoning is based on the theory of harmonic vector fields on the tangent spaces as Riemannian manifolds or, in an equivalent way, as Minkowski spaces. Our main result states that the conformal equivalence between two Berwald manifolds must be trivial unless the manifolds are Riemannian. 相似文献
12.
Franz J. Pedit 《Annals of Global Analysis and Geometry》1987,5(3):199-215
We show that a compact flat manifold has the structure of a real affine variety. Using generators of the affine algebra we constructed embeddings with flat induced metric of all compact flat manifolds with cyclic holonomy group of order 2. 相似文献
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I. G. Nikolaev 《Commentarii Mathematici Helvetici》1995,70(1):210-234
Schur's theorem states that an isotropic Riemannian manifold of dimension greater than two has constant curvature. It is natural
to guess that compact almost isotropic Riemannian manifolds of dimension greater than two are close to spaces of almost constant
curvature. We take the curvature anisotropy as the discrepancy of the sectional curvatures at a point. The main result of
this paper is that Riemannian manifolds in Cheeger's class ℜ(n,d,V,A) withL
1-small integral anisotropy haveL
p-small change of the sectional curvature over the manifold. We also estimate the deviation of the metric tensor from that
of constant curvature in theW
p
2
-norm, and prove that compact almost isotropic spaces inherit the differential structure of a space form. These stability
results are based on the generalization of Schur' theorem to metric spaces. 相似文献
15.
A. S. Galaev 《Siberian Mathematical Journal》2013,54(4):604-613
The existence of a recurrent spinor field on a pseudo-Riemannian spin manifold (M,g) is closely related to the existence of a parallel 1-dimensional complex subbundle of the spinor bundle of (M,g). We characterize the following simply connected pseudo-Riemannian manifolds that admit these subbundles in terms of their holonomy algebras: Riemannian manifolds, Lorentzian manifolds, pseudo-Riemannian manifolds with irreducible holonomy algebras, and pseudo-Riemannian manifolds of neutral signature admitting two complementary parallel isotropic distributions. 相似文献
16.
The classification of restricted holonomy groups of \(n\) -dimensional Lorentzian manifolds was obtained about ten years ago. However, up to now, not much is known about the structure of the full holonomy group. In this paper we study the full holonomy group of Lorentzian manifolds with a parallel null line bundle. Based on the classification of the restricted holonomy groups of such manifolds, we prove several structure results about the full holonomy. We establish a construction method for manifolds with disconnected holonomy starting from a Riemannian manifold and a properly discontinuous group of isometries. This leads to a variety of examples, most of them being quotients of pp-waves with disconnected holonomy, including a non-flat Lorentzian manifold with infinitely generated holonomy group. Furthermore, we classify the full holonomy groups of solvable Lorentzian symmetric spaces and of Lorentzian manifolds with a parallel null spinor. Finally, we construct examples of globally hyperbolic manifolds with complete spacelike Cauchy hypersurfaces, disconnected full holonomy and a parallel spinor. 相似文献
17.
Given a polarized manifold there are obstructions for asymptotic Chow semistability described as integral invariants which can be regarded as characters of the Lie algebra of holomorphic vector fields. In this paper we show that, on toric Fano manifolds, the linear span of those Lie algebra characters coincides with the derivatives of the Laurent series of the Hilbert series. 相似文献
18.
A class of manifolds which admit an f-structure with s-dimensional parallelizable kernel is introduced and studied. Such manifolds are Kenmotsu manifolds if s = 1, and carry a locally conformal K?hler structure of Kashiwada type when s = 2. The existence of several foliations allows to state some local decomposition theorems. The Ricci tensor together with
Einstein-type conditions and f-sectional curvatures are also considered. Furthermore, each manifold carries a homogeneous Riemannian structure belonging
to the class
of the classification stated by Tricerri and Vanhecke, provided that it is a locally symmetric space.
Dedicated to the memory of Professor Aldo Cossu 相似文献
19.
In this paper we study almost Hermitian submersions with total space a locally conformal Kähler (l.c.K.) manifold, i.e., l.c.K. submersions. We derive necessary and sufficient conditions for the fibers of a l.c.K. submersion to be minimal and for the horizontal distribution to be completely integrable. We give, under certain conditions, some relations between the Betti numbers of the total space and the base space of a l.c.K. submersion and we obtain all the l.c.K. submersions with totally geodesic fibers and total space a particular class of generalized Hopf manifolds.Supported by the Consejería de Educación del Gobierno de Canarias 相似文献
20.
Lorenz J. Schwachhöfer 《Annals of Global Analysis and Geometry》2000,18(3-4):291-308
Much of the early work of Alfred Gray was concerned with the investigation of Riemannian manifolds with special holonomy, one of the most vivid fields of Riemannian geometry in the 1960s and the following decades. It is the purpose of the present article to give a brief summary and an appreciation of Gray's contributions in this area on the one hand, and on the other hand to describe some of the more recent developments in the theory of non-Riemannian or,more specifically, symplectic holonomy groups. Namely, we show that the Merkulov twistor space of a connection on a symplectic manifold M whose holonomy group is irreducible and properly contained in Sp(V) consists of maximal totally geodesic Lagrangian submanifolds of M. 相似文献