共查询到20条相似文献,搜索用时 15 毫秒
1.
M. Yu. Nikanorova 《Journal of Mathematical Sciences》2007,140(4):582-588
The structure of the tangent bundle of the real Grassmann manifold G
+
p,n
under the Plücker embedding (in the exterior algebra of the initial Euclidean space) is studied. Explicit expressions for
the relation between decompositions of a tangent vector with respect to different bases of the tangent space are obtained,
and a constructivemethod yielding the canonical (= simplest) decomposition is presented. Bibliography: 8 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 329, 2005, pp. 147–158. 相似文献
2.
3.
A. N. Glushakov 《Journal of Mathematical Sciences》2000,100(3):2189-2193
The Plücker model of the Grassmann manifold G
p,p+q
+
is considered. The structure of intersections of G
p,p+q
+
with tangent spaces of G
p,p+q
+
regarded as subspaces of the ambient exterior algebra is described. An explicit formula for the second fundamental form of
G
2,4
+
as of a hypersurface in the five-dimensional sphere is given. The level sets of the normal curvature functions for this hypersurface
are studied. Bibliography: 3 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 246, 1997, pp. 5–12.
Translated by N. Yu. Netsvetaev. 相似文献
4.
Shintar? Kuroki 《Transformation Groups》2011,16(2):481-536
The purpose of this paper is to classify torus manifolds (M
2n
, T
n
) with codimension one extended G-actions (M
2n
, G) up to essential isomorphism, where G is a compact, connected Lie group whose maximal torus is T
n
. For technical reasons, we do not assume torus manifolds are orientable. We prove that there are seven types of such manifolds.
As a corollary, if a nonsingular toric variety or a quasitoric manifold has a codimension one extended action then such manifold
is a complex projective bundle over a product of complex projective spaces. 相似文献
5.
Julien Grivaux 《Journal of Geometric Analysis》2006,16(3):523-533
We prove that Tian’s invariant on the complex Grassmann manifold G p,q(?)is equal to 1/(p+ q).The method introduced here uses a Lie group of holomorphic isometries which operates transitively on the considered manifolds and a natural imbedding of (?1 (?))p in G p,q (?). 相似文献
6.
LetG n,k denote the Grassmann manifold ofk-planes in ?n. We show that for any continuous mapf: G n,k→Gn,l the induced map inZ/2-cohomology is either zero in positive dimensions or has image in the subring generated by w1(γn, k), provided 1≤l<k≤[n/2] andn≥k+2l-1. Our main application is to obtain negative results on the existence of equivariant maps between oriented Grassmann manifolds. We also obtain positive results in many cases on the existence of equivariant maps between oriented Grassmann manifolds. 相似文献
7.
Michal Sadowski 《Central European Journal of Mathematics》2004,2(2):332-338
Let E
Aff(Γ,G, m) be the set of affine equivalence classes of m-dimensional complete flat manifolds with a fixed fundamental group Γ and a fixed holonomy group G. Let n be the dimension of a closed flat manifold whose fundamental group is isomorphic to Γ. We describe E
Aff(Γ,G, m) in terms of equivalence classes of pairs (ε, ρ), consisting of epimorphisms of Γ onto G and representations of G in ℝ
m-n
. As an application we give some estimates of card E
Aff(Γ,G, m). 相似文献
8.
Yoshinobu Kamishima 《Central European Journal of Mathematics》2012,10(5):1771-1788
An (m+2)-dimensional Lorentzian similarity manifold M is an affine flat manifold locally modeled on (G,ℝ m+2), where G = ℝ m+2 ⋊ (O(m+1, 1)×ℝ+). M is also a conformally flat Lorentzian manifold because G is isomorphic to the stabilizer of the Lorentzian group PO(m+2, 2) of the Lorentz model S m+1,1. We discuss the properties of compact Lorentzian similarity manifolds using developing maps and holonomy representations. 相似文献
9.
S. E. Kozlov 《Journal of Mathematical Sciences》2000,100(3):2239-2253
The paper deals with the properties of the exterior algebra ℝ(Λn) related to the Euclidean structure on ℝ(Λn) induced by the scalar product in ℝ(Λn). A geometric interpretation of inner multiplication for simple p-vectors is given. An invariant form of the Cartan criterion
for the simplicity of a p-vector is given. The Plücker model realizing the real Grassmann manifold as a submanifold of the
Euclidean space ℝ(Λn), and an isometry of this submanifold onto the classical Grassmann manifold with SO(n)-invariant metric are described. A
canonical decomposition of bivectors is given. Bibliography: 12 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 246, 1997, pp. 84–107.
Translated by N. Yu: Netsvetaev. 相似文献
10.
Philip L. Bowers 《Topology and its Applications》1984,17(2):173-187
It is shown that if G is an arbitrary upper semicontinuous decomposition of En for which π(NG embeds in Sm for some m?3, then the decomposition space embeds as a closed subset of En+m+1. The proof consists of constructing a cell-like upper semicontinuous decomposition G? of En+m+1 which intersects En to yield precisely G and using Edwards' Cell-Like Approximation Theorem to show that G? is shrinkable. As an immediate corollary, embeds in En+2k+2 whenever G is an arbitrary k-dimensional upper semicontinuous decomposition of En. This is an improvement of (n?1)-dimensions over the corresponding dimension theoretic result and examples due to Daverman show that this result is sharp in case n is odd and off by no more than one dimension in case n is even. 相似文献
11.
Katsusuke Sekiguchi 《代数通讯》2013,41(11):3611-3623
For a prime p, we denote by Bn the cyclic group of order pn. Let φ be a faithful irreducible character of Bn, where p is an odd prime. We study the p-group G containing Bn such that the induced character φG is also irreducible. The purpose of this article is to determine the subgroup NG(NG(Bn)) of G under the hypothesis [NG(Bn):Bn]4 ≦ pn. 相似文献
12.
Yoshinobu Kamishima 《Central European Journal of Mathematics》2014,12(6):861-878
We introduce conformally flat Fefferman-Lorentz manifold of parabolic type as a special class of Lorentz parabolic manifolds. It is a smooth (2n+2)-manifold locally modeled on (Û(n+1, 1), S 2n+1,1). As the terminology suggests, when a Fefferman-Lorentz manifold M is conformally flat, M is a Fefferman-Lorentz manifold of parabolic type. We shall discuss which compact manifolds occur as a conformally flat Fefferman-Lorentz manifold of parabolic type. 相似文献
13.
The (4n+3)-dimensional sphere S4n+3 can be viewed as the boundary of the quaternionic hyperbolic space and the group PSp(n+1,1) of quaternionic hyperbolic isometries extends to a real analytic transitive action on S4n+3. We call the pair (PSp(n+1,1),S4n+3) a spherical Q C-C geometry. A manifold M locally modelled on this geometry is said to be a spherical Q C-C manifold. We shall classify all pairs (G,M) where G is a three-dimensional connected Lie group which acts smoothly and almost freely on a compact spherical Q C-C manifold M, preserving the geometric structure. As an application, we shall determine all compact 3-pseudo-Sasakian manifolds admitting spherical Q C-C structures. 相似文献
14.
V. N. Berestovskiĭ 《Siberian Advances in Mathematics》2014,24(1):12-17
In this article, we introduce a newclass of compact homogeneous Riemannian manifolds (M = G/H, µ) almost normal with respect to a transitive Lie group G of isometries for which by definition there exists a G-left-invariant and an H-right-invariant inner product ν such that the canonical projection p: (G, ν) → (G/H, µ) is a Riemannian submersion and the norm | · | of the product ν is at least the bi-invariant Chebyshev normon G defined by the space (M,µ).We prove the following results: Every homogeneous Riemannian manifold is almost normal homogeneous. Every homogeneous almost normal Riemannian manifold is naturally reductive and generalized normal homogeneous. For a homogeneous G-normal Riemannian manifold with simple Lie group G, the unit ball of the norm | · | is a Löwner-John ellipsoid with respect to the unit ball of the Chebyshev norm; an analogous assertion holds for the restrictions of these norms to a Cartan subgroup of the Lie group G. Some unsolved problems are posed. 相似文献
15.
In this paper, we first present an O(n+m)-time sequential algorithm to solve the Hamiltonian problem on a distance-hereditary graph G, where n and m are the number of vertices and edges of G, respectively. This algorithm is faster than the previous best known algorithm for the problem which takes O(n2) time. We also give an efficient parallel implementation of our sequential algorithm. Moreover, if G is represented by its decomposition tree form, the problem can be solved optimally in O(logn) time using O((n+m)/logn) processors on an EREW PRAM. 相似文献
16.
J.P. May 《Journal of Pure and Applied Algebra》1982,26(1):1-69
Let G be a finitely presented group given by its pre-abelian presentation <X1,…,Xm; Xe11ζ1,…,Xemmζ,ζm+1,…>, where ei≥0 for i = 1,…, m and ζj?G′ for j≥1. Let N be the subgroup of G generated by the normal subgroups [xeii, G] for i = 1,…, m. Then Dn+2(G)≡γn+2(G) (modNG′) for all n≥0, where G” is the second commutator subgroup of G,γn+2(G) is the (n+2)th term of the lower central series of G and Dn+2(G) = G∩(1+△n+2(G)) is the (n+2)th dimension subgroup of G. 相似文献
17.
We present the construction for a u-product G1 ○ G2 of two u-groups G1 and G2, and prove that G1 ○ G2 is also a u-group and that every u-group, which contains G1 and G2 as subgroups and is generated by these, is a homomorphic image of G1 ○ G2. It is stated that if G is a u-group then the coordinate group of an affine space Gn is equal to G ○ Fn, where Fn is a free metabelian group of rank n. Irreducible algebraic sets in G are treated for the case where G is a free metabelian
group or wreath product of two free Abelian groups of finite ranks.
__________
Translated from Algebra i Logika, Vol. 44, No. 5, pp. 601–621, September–October, 2005.
Supported by RFBR grant No. 05-01-00292, by FP “Universities of Russia” grant No. 04.01.053, and by RF Ministry of Education
grant No. E00-1.0-12. 相似文献
18.
V. Maiorov 《Advances in Computational Mathematics》2006,25(4):435-450
We consider the manifolds H
n(φ) formed by all possible linear combinations of n functions from the set {φ(A⋅+b)}, where x→Ax+b is arbitrary affine mapping in the space ℝd. For example, neural networks and radial basis functions are the manifolds of type H
n(φ). We obtain estimates for pseudo-dimension of the manifold H
n(φ) for wide collection of the generator function φ. The estimates have the order O(d
2
n) in degree scale, that is the order is proportional to number of parameters of the manifold H
n(φ). Moreover the estimates for ɛ-entropy of the manifold H
n(φ) are obtained.
Mathematics subject classifications (2000) 41A46, 41A50, 42A61, 42C10
V. Maiorov: Supported by the Center for Absorption in Science, Ministry of Immigrant Absorption, State of Israel. 相似文献
19.
L. P. Plakhta 《Journal of Mathematical Sciences》1993,64(5):1121-1124
It is shown that a functor of G-symmetric degree maps closed 2-manifolds into manifolds if and only if it is isomorphic to the Cartesian product of functors of symmetric degree. We study the canonical stratification of the pseudomanifolds
, where M is a closed orientable surface. We find the torsion subgroups of certain homology groups Hi(SP
G
n
M,).Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 32, 1990, pp. 9–14. 相似文献
20.
Let F
p,t
(n) denote the number of the coefficients of (x
1+1x
2+...+x
t
)
j
, 0 ≤j≤n− 1, which are not divisible by the prime p. Define G
p,t
(n) = F
p,t
/n
θ and β(p,t) = lim infF
p,t
)(n)/n
θ, where θ = (log)/(log p). In this paper, we mainly prove that G
p,t
can be extended to a continuous function on ℝ+, and the function G
p,t
is nowhere monotonic. Both the set of differential points of the function G
p,t
and the set of non-differential points of the function G
p,t
are dense in ℝ+.
Received February 18, 2000, Accepted December 7, 2000 相似文献