共查询到20条相似文献,搜索用时 31 毫秒
1.
V. V. Gorbatsevich 《Siberian Mathematical Journal》2001,42(6):1036-1046
We consider the isometry groups of Riemannian solvmanifolds and also study a wider class of homogeneous aspheric Riemannian spaces. We clarify the topological structure of these spaces (Theorem 1). We demonstrate that each Riemannian space with a maximally symmetric metric admits an almost simply transitive action of a Lie group with triangular radical (Theorem 2). We apply this result to studying the isometry groups of solvmanifolds and, in particular, solvable Lie groups with some invariant Riemannian metric. 相似文献
2.
Ignacio Bajo 《Annals of Global Analysis and Geometry》1996,14(1):61-67
We describe a family of non-nilpotent Riemannian solvable Lie groups whose isotropy group has a prescribed compact Lie algebra. 相似文献
3.
André Diatta 《Geometriae Dedicata》2008,133(1):83-94
We investigate contact Lie groups having a left invariant Riemannian or pseudo-Riemannian metric with specific properties
such as being bi-invariant, flat, negatively curved, Einstein, etc. We classify some of such contact Lie groups and derive
some obstruction results to the existence of left invariant contact structures on Lie groups.
相似文献
4.
Mohamed Boucetta 《Journal of the Egyptian Mathematical Society》2011,19(1-2):57-70
We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting. We give also some new results on the integrability of Riemannian Lie algebroids. 相似文献
5.
Tunahan Turhan 《Mathematical Methods in the Applied Sciences》2020,43(5):2747-2758
We study magnetic trajectories in Lie groups equipped with bi-invariant Riemannian metric. We define the Lorentz force of a magnetic field in a Lie group G, and then, we give the Lorentz force equation for the associated magnetic trajectories that are curves in G. When the manifold is a Lie group G equipped with bi-invariant Riemannian metric, we derive differential equation system that characterizes magnetic flow associated with the Killing magnetic curves with regard to the Lie reduction of the curve γ in G. 相似文献
6.
Ron Karidi 《Geometriae Dedicata》1993,46(3):249-277
We discuss left invariant Riemannian metrics on Lie groups, and the Ricci structures they induce. A computational approach is used to manipulate the curvature tensors, and construct perturbations which preserve the Ricci structure but not the (algebraic) Lie structure. We show that this method can lead to significant changes in the growth of volume. We also show that this approach may be used to reduce the complexity of some curvature computations in Lie groups. 相似文献
7.
The article presents an information about the Laplace operator defined on the real-valued mappings of compact Riemannian manifolds,
and its spectrum; some properties of the latter are studied. The relationship between the spectra of two Riemannian manifolds
connected by a Riemannian submersion with totally geodesic fibers is established. We specify a method of calculating the spectrum
of the Laplacian for simply connected simple compact Lie groups with biinvariant Riemannian metrics, by representations of
their Lie algebras. As an illustration, the spectrum of the Laplacian on the group SU(2) is found. 相似文献
8.
Four-dimensional locally homogeneous Riemannian manifolds are either locally symmetric or locally isometric to Riemannian Lie groups. We determine how and to what extent this result holds in the Lorentzian case. 相似文献
9.
Božidar Jovanović 《Regular and Chaotic Dynamics》2011,16(5):504-513
We prove the integrability of geodesic flows on the Riemannian g.o. spaces of compact Lie groups, as well as on a related
class of Riemannian homogeneous spaces having an additional principal bundle structure. 相似文献
10.
We present a new method for manufacturing complex-valued harmonic morphisms from a wide class of Riemannian Lie groups. This
yields new solutions from an important family of homogeneous Hadamard manifolds. We also give a new method for constructing
left-invariant foliations on a large class of Lie groups producing harmonic morphisms. 相似文献
11.
Evangelia Samiou 《manuscripta mathematica》2002,107(1):101-110
We construct a family of simply connected 2-step nilpotent Lie groups of higher rank such that every geodesic lies in a flat.
These are as Riemannian manifolds irreducible and arise from real representations of compact Lie algebras. Moreover we show
that groups of Heisenberg type do not even infinitesimally have higher rank.
Received: 2 July 2001 / Revised version: 19 October 2001 相似文献
12.
《Indagationes Mathematicae》2019,30(4):669-705
In this paper, we define locally convex vector spaces of weighted vector fields and use them as model spaces for Lie groups of weighted diffeomorphisms on Riemannian manifolds. We prove an easy condition on the weights that ensures that these groups contain the compactly supported diffeomorphisms. We finally show that for the special case where the manifold is the euclidean space, these Lie groups coincide with the ones constructed in the author’s earlier work (Walter, 2012). 相似文献
13.
Gabriel Teodor Pripoae 《Comptes Rendus Mathematique》2006,342(11):865-868
We study to what extent vector fields on Lie groups may be considered as geodesic fields. For a given left invariant vector field on a Lie group, we prove there exists a Riemannian metric whose geodesics are its trajectories. When we consider left invariant metrics, differences between the Riemannian and the Lorentzian cases appear, coded by properties of the Lie algebra. To cite this article: G.T. Pripoae, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
14.
We study the spaces of left-invariant Riemannian metrics on a Lie group up to isometry, and up to isometry and scaling. In this paper, we see that such spaces can be identified with the orbit spaces of certain isometric actions on noncompact symmetric spaces. We also study some Lie groups whose spaces of left-invariant metrics up to isometry and scaling are small. 相似文献
15.
We study three-dimensional generalized Ricci solitons, both in Riemannian and Lorentzian settings. We shall determine their homogeneous models, classifying left-invariant generalized Ricci solitons on three-dimensional Lie groups. 相似文献
16.
We obtain a complete classification of all the possible values of the signature of the Ricci curvature of left-invariant Riemannian
metrics on four-dimensional nonunimodular Lie groups. 相似文献
17.
We introduce the notion of geometrical engagement for actions of semisimple Lie groups and their lattices as a concept closely
related to Zimmer's topological engagement condition. Our notion is a geometrical criterion in the sense that it makes use
of Riemannian distances. However, it can be used together with the foliated harmonic map techniques introduced in [8] to establish
foliated geometric superrigidity results for both actions and geometric objects. In particular, we improve the applications
of the main theorem in [9] to consider nonpositively curved compact manifolds (not necessarily with strictly negative curvature).
We also establish topological restrictions for Riemannian manifolds whose universal cover have a suitable symmetric de Rham
factor (Theorem B), as well as geometric obstructions for nonpositively curved compact manifolds to have fundamental groups
isomorphic to certain groups build out of cocompact lattices in higher rank simple Lie groups (Corollary 4.5).
Received: October 22, 1997 相似文献
18.
We obtain a complete classification of all the possible values of the signature of the Ricci curvature of left-invariant Riemannian
metrics on four-dimensional unimodular Lie groups. 相似文献
19.
Mathematische Annalen - We classify representations of compact connected Lie groups whose induced action on the unit sphere has the orbit space isometric to a Riemannian orbifold. 相似文献
20.
JOONKOOK SHIN 《Geometriae Dedicata》1997,65(3):267-290
We characterize the left-invariant Riemannian metrics on each of the six unimodular simply connected 3-dimensional Lie groups which give rise to 3-, 4-, or 6-dimensional isometry groups. It turns out that this classification is independent of curvature properties. 相似文献