共查询到20条相似文献,搜索用时 31 毫秒
1.
We prove that every locally connected quotient G/H of a locally compact, connected, first countable topological group G by
a compact subgroup H admits a G-invariant inner metric with curvature bounded below. Every locally compact homogeneous space
of curvature bounded below is isometric to such a space. These metric spaces generalize the notion of Riemannian homogeneous
space to infinite dimensional groups and quotients which are never (even infinite dimensional) manifolds. We study the geometry
of these spaces, in particular of non-negatively curved homogeneous spaces.
Dedicated to the memory of A. D. Alexandrov 相似文献
2.
A Riemannian g.o. manifold is a homogeneous Riemannian manifold (M,g) on which every geodesic is an orbit of a one-parameter group of isometries. It is known that every simply connected Riemannian g.o. manifold of dimension ?5 is naturally reductive. In dimension 6 there are simply connected Riemannian g.o. manifolds which are in no way naturally reductive, and their full classification is known (including compact examples). In dimension 7, just one new example has been known up to now (namely, a Riemannian nilmanifold constructed by C. Gordon). In the present paper we describe compact irreducible 7-dimensional Riemannian g.o. manifolds (together with their “noncompact duals”) which are in no way naturally reductive. 相似文献
3.
Daniel Guan 《Journal of Geometric Analysis》2002,12(1):63-79
We consider the existence of Calabi extremal metrics on certain compact almost homogeneous manifold of cohomogeneity one.
We proved that the positivity of the generalized Futaki invariant implies the existence. We expect that the converse is also
true for all this kind of manifolds. 相似文献
4.
Fabio Podestà 《Monatshefte für Mathematik》1996,122(3):215-225
This work deals with positively curved compact Riemannian manifolds which are acted on by a closed Lie group of isometries whose principal orbits have codimension one and are isotropy irreducible homogeneous spaces. For such manifolds we can show that their universal covering manifold may be isometrically immersed as a hypersurface of revolution in an euclidean space. 相似文献
5.
We construct examples of symplectic half-flat manifolds on compact quotients of solvable Lie groups. We prove that the Calabi-Yau
structures are not rigid in the class of symplectic half-flat structures. Moreover, we provide an example of a compact 6-dimensional
symplectic half-flat manifold whose real part of the complex volume form is d-exact. Finally we discuss the 4-dimensional case.
This work was supported by the Projects M.I.U.R. “Geometric Properties of Real and Complex Manifolds”, “Riemannian Metrics
and Differentiable Manifolds” and by G.N.S.A.G.A. of I.N.d.A.M. 相似文献
6.
7.
V.N. Berestovski? 《Differential Geometry and its Applications》2011,29(4):533-546
The authors give a short survey of previous results on generalized normal homogeneous (δ-homogeneous, in other terms) Riemannian manifolds, forming a new proper subclass of geodesic orbit spaces with nonnegative sectional curvature, which properly includes the class of all normal homogeneous Riemannian manifolds. As a continuation and an application of these results, they prove that the family of all compact simply connected indecomposable generalized normal homogeneous Riemannian manifolds with positive Euler characteristic, which are not normal homogeneous, consists exactly of all generalized flag manifolds Sp(l)/U(1)⋅Sp(l−1)=CP2l−1, l?2, supplied with invariant Riemannian metrics of positive sectional curvature with the pinching constants (the ratio of the minimal sectional curvature to the maximal one) in the open interval (1/16,1/4). This implies very unusual geometric properties of the adjoint representation of Sp(l), l?2. Some unsolved questions are suggested. 相似文献
8.
Let G be a compact Lie group acting isometrically on a compact Riemannian manifold M with nonempty fixed point set M
G
. We say that M is fixed-point homogeneous if G acts transitively on a normal sphere to some component of M
G
. Fixed-point homogeneous manifolds with positive sectional curvature have been completely classified. We classify nonnegatively
curved fixed-point homogeneous Riemannian manifolds in dimensions 3 and 4 and determine which nonnegatively curved simply-connected
4-manifolds admit a smooth fixed-point homogeneous circle action with a given orbit space structure. 相似文献
9.
In the first part of this article, we prove an explicit lower bound on the distance to the cut point of an arbitrary geodesic
in a simply connected two-step nilpotent Lie group G with a lieft invariant metric. As a result, we obtaine a lower bound
on the injectivity radius of a simply connected two-step nilpotent Lie group with a left invariant metric. We use this lower
bound to determine the form of certain length minimizing geodesics from the identity to elements in the center of G. We also
give an example of a two-step nilpotent Lie group G such that along most geodesics in this group, the cut point and the first
conjugate point do not coincide. In the second part of this article, we examine the relation between the Laplace spectrum
and the length spectrum on nilmanifolds by showing that a method developed by Gordon and Wilson for constructing families
of isospectral two-step nilmanifolds necessarily yields manifolds with the same length spectrum. As a consequence, all known
methods for constructing families of isospectral two-step nilmanifolds necessarily yield manifolds with the same length spectrum.
In memory of Robert Brooks 相似文献
10.
Let X be a connected compact complex manifold. We call X a homogeneous manifold if there exists a complex Liegroup G of biholomorphic automorphisms of X such that for any two points p, qX there is a gG with: g(p)=q. We give some non-trivial examples of homogeneous manifolds. All examples are non-kaehlerian manifolds. Such examples have been given first by Iwasawa (as far as we know). The last section of this note contains a proposition, which shows that only very special non-semisimple Liegroups are able to act transitivily in the sense stated above, on a compact complex manifold. This is remarkable also in contrast to the semisimple case (cf. [3]). 相似文献
11.
《中国科学 数学(英文版)》2015,(7)
In this paper, we find some new homogeneous manifolds G/H admitting non-Riemannian EinsteinRanders metrics when G is the compact simple Lie group E6, or E7 or E8. In the beginning, we prove that these homogeneous manifolds admit Riemannian Einstein metrics. Based on these metrics, we obtain non-Riemannian Einstein Randers metrics on them. 相似文献
12.
Grzegorz Graff Agnieszka Kaczkowska Piotr Nowak-Przygodzki Justyna Signerska 《Topology and its Applications》2012,159(10-11):2728-2735
Let f be a self-map of a compact connected manifold M. We characterize Lefschetz periodic point free continuous self-maps of M for several classes of manifolds and generalize the results of Guirao and Llibre [J.L.G. Guirao, J. Llibre, On the Lefschetz periodic point free continuous self-maps on connected compact manifolds, Topology Appl. 158 (16) (2011) 2165–2169]. 相似文献
13.
We generalize the notion of fixed point homogeneous isometric group actions to the context of singular Riemannian foliations. We find that in some cases, positively curved manifolds admitting these so-called point leaf maximal SRF's are diffeo/homeomorphic to compact rank one symmetric spaces. In all cases, manifolds admitting such foliations are cohomology CROSSes or finite quotients of them. Among non-simply connected manifolds, we find examples of such foliations which are non-homogeneous. 相似文献
14.
Each element $x$ of the commutator subgroup $[G, G]$ of a group $G$
can be represented as a product of commutators. The minimal number
of factors in such a product is called the commutator length of
$x$. The commutator length of $G$ is defined as the supremum of
commutator lengths of elements of $[G, G]$.
We show that for certain closed symplectic manifolds $(M,\omega)$,
including complex projective spaces and Grassmannians,
the universal cover $\widetilde{\hbox{\rm Ham}\, (M,\omega)$ of the group of Hamiltonian
symplectomorphisms of $(M,\omega)$ has infinite
commutator length. In particular, we present explicit examples of
elements in $\widetilde{\hbox{\rm Ham}\, (M,\omega)$ that have
arbitrarily large
commutator length -- the estimate on their commutator length
depends on the multiplicative structure of the quantum cohomology
of $(M,\omega)$. By a different method we also show that in the
case $c_1 (M) = 0$ the group
$\widetilde{\hbox{\rm Ham}\, (M,\omega)$ and the universal cover
${\widetilde{\Symp}}_0\, (M,\omega)$ of the identity
component of the group of symplectomorphisms of $(M,\omega)$
have infinite commutator length. 相似文献
15.
16.
We study and classify a large class of minimal orbits in complex flag manifolds for the holomorphic action of a real Lie group. These orbits are all symmetric CR spaces for the restriction of a suitable class of Hermitian invariant metrics on the ambient flag manifold. As a particular case we obtain that the standard compact homogeneous CR manifolds associated with semisimple Levi-Tanaka algebras are symmetric CR-spaces. 相似文献
17.
Fabrice Baudoin 《Bulletin des Sciences Mathématiques》2002,126(6):481-491
We show that the only compact simply connected manifolds for which the radial part of Brownian motion enjoys the Markov property are compact two points homogeneous spaces, i.e. rank one symmetric spaces. 相似文献
18.
We construct pairs of conformally equivalent isospectral Riemannian metrics ?1g and ?2g on spheres Sn and balls Bn+1 for certain dimensions n, the smallest of which is n=7, and on certain compact simple Lie groups. In the case of Lie groups, the metric g is left-invariant. In the case of spheres and balls, the metric g not the standard metric but may be chosen arbitrarily close to the standard one. For the same manifolds (M, g) we also show that the functions ?1 and ?2 are isospectral potentials for the Schrödinger operator ?2\gD + \gf. To our knowledge, these are the first examples of isospectral potentials and of isospectral conformally equivalent metrics on simply connected closed manifolds. 相似文献
19.
We study isospectrality on p-forms of compact flat manifolds by using the equivariant spectrum of the Hodge-Laplacian on the torus. We give an explicit formula for the multiplicity of eigenvalues and a criterion for isospectrality. We construct a variety of new isospectral pairs, some of which are the first such examples in the context of compact Riemannian manifolds. For instance, we give pairs of flat manifolds of dimension n=2p, p≥2, not homeomorphic to each other, which are isospectral on p-forms but not on q-forms for q∈p, 0≤q≤n. Also, we give manifolds isospectral on p-forms if and only if p is odd, one of them orientable and the other not, and a pair of 0-isospectral flat manifolds, one of them Kähler, and the other not admitting any Kähler structure. We also construct pairs, M, M′ of dimension n≥6, which are isospectral on functions and such that βp(M)<βp(M’), for 0
4 and ? 2 2 , respectively. 相似文献
20.
We study curvatures of homogeneous Randers spaces. After deducing the coordinate-free formulas of the flag curvature and Ricci scalar of homogeneous Randers spaces, we give several applications. We first present a direct proof of the fact that a homogeneous Randers space is Ricci quadratic if and only if it is a Berwald space. We then prove that any left invariant Randers metric on a non-commutative nilpotent Lie group must have three flags whose flag curvature is positive, negative and zero, respectively. This generalizes a result of J.A. Wolf on Riemannian metrics. We prove a conjecture of J. Milnor on the characterization of central elements of a real Lie algebra, in a more generalized sense. Finally, we study homogeneous Finsler spaces of positive flag curvature and particularly prove that the only compact connected simply connected Lie group admitting a left invariant Finsler metric with positive flag curvature is SU(2). 相似文献