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1.
We study m-dimensional real submanifolds M with (m − 1)-dimensional maximal holomorphic tangent subspace in complex projective space. On these manifolds there exists an almost
contact structure F which is naturally induced from the ambient space and in this paper we study the condition h(FX, Y) − h(X, FY) = g(FX, Y)η, η ∈ T
⊥(M), on the almost contact structure F and on the second fundamental form h of these submanifolds and we characterize certain model spaces in complex projective space. 相似文献
2.
Real hypersurfaces of a complex manifold admit a naturally induced almost contact structure F′ from the almost complex structure of the ambient manifold. We prove that for any F′-invariant submanifold M of a geodesic hypersphere in a non-flat complex space form and of a horosphere in a complex hyperbolic space, its second
fundamental form h satisfies the condition h(FX,Y ) - h(X, FY) = g(FX, Y )h, X,Y ? T(M), 0 1 h ? T^(M){h(FX,Y ) - h(X, FY) = g(FX, Y )\eta, X,Y \in T(M), 0 \ne \eta \in {T^\perp}(M)}, which has been considered in [2] and [3]. 相似文献
3.
Mirjana Djori? 《Journal of Mathematical Analysis and Applications》2009,356(1):237-241
Considering n-dimensional real submanifolds M of a complex space form which are CR submanifolds of CR dimension , we study the condition h(FX,Y)+h(X,FY)=0 on the structure tensor F naturally induced from the almost complex structure J of the ambient manifold and on the second fundamental form h of submanifolds M. 相似文献
4.
We consider a (2m + 3)-dimensional Riemannian manifold M(ξ r, ηr, g ) endowed with a vertical skew symmetric almost contact 3-structure. Such manifold is foliated by 3-dimensional submanifolds
of constant curvature tangent to the vertical distribution and the square of the length of the vertical structure vector
field is an isoparametric function. If, in addition, M(ξ r, ηr, g ) is endowed with an f -structure φ, M, turns out to be a framed f−CR-manifold. The fundamental 2-form Ω associated with φ is a presymplectic form. Locally, M is the Riemannian product
of two totally geodesic submanifolds, where
is a 2m-dimensional Kaehlerian submanifold and
is a 3-dimensional submanifold of constant curvature. If M is not compact, a class of local Hamiltonians of Ω is obtained. 相似文献
5.
We treat n-dimensional compact minimal submanifolds of complex projective space when the maximal holomorphic tangent subspace is (n − 1)-dimensional and we give a sufficient condition for such submanifolds to be tubes over totally geodesic complex subspaces.
Authors’ addresses: Mirjana Djorić, Faculty of Mathematics, University of Belgrade, Studentski trg 16, pb. 550, 11000 Belgrade,
Serbia; Masafumi Okumura, 5-25-25 Minami Ikuta, Tama-ku, Kawasaki, Japan 相似文献
6.
SoitM(Ω, η, ξ,g) une variété à (2m+1)-dimensions presque cosymplectique (i. e. Ω∈Λ2
M est de rang 2m et Ω
m
Λη≠0). On définitM comme étant une variété semi-cosymplectique si en termes ded
ω-cohomologie la paire (Ω, η) satisfait àdη=0,d
−cη Ω=Ψ∈Λ3
M,c=constant. Dans ce cas le champ vectoriel de structure ξ=b
−1(η) est un champ conforme horizontal et siM est une forme-espace elle est nécessairement du type hyperbolique. Différentes propriétés de cette structure sont étudiés
et le cas oùM est une variété para Sasakienne dans le sens large est discuté. 相似文献
7.
Mayuko Kon 《Czechoslovak Mathematical Journal》2008,58(4):1279-1287
We give a characterization of totally η-umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form in terms of totally umbilical condition
for the holomorphic distribution on real hypersurfaces. We prove that if the shape operator A of a real hypersurface M of a complex space form M
n
(c), c ≠ 0, n ⩾ 3, satisfies g(AX, Y) = ag(X, Y) for any X, Y ∈ T
0(x), a being a function, where T
0 is the holomorphic distribution on M, then M is a totally η-umbilical real hypersurface or locally congruent to a ruled real hypersurface. This condition for the shape operator is a
generalization of the notion of η-umbilical real hypersurfaces. 相似文献
8.
Assuming m − 1 < kp < m, we prove that the space C
∞(M, N) of smooth mappings between compact Riemannian manifolds M, N (m = dim M) is dense in the Sobolev space W
k,p
(M, N) if and only if π
m−1(N) = {0}. If π
m−1(N) ≠ {0}, then every mapping in W
k,p
(M, N) can still be approximated by mappings M → N which are smooth except in finitely many points. 相似文献
9.
Lin Feng Wang 《Annals of Global Analysis and Geometry》2012,42(1):79-89
Let M be an n-dimensional complete noncompact Riemannian manifold, h be a smooth function on M and dμ = e
h
dV be the weighted measure. In this article, we prove that when the spectrum of the weighted Laplacian
\trianglem{\triangle_{\mu}} has a positive lower bound λ1(M) > 0 and the m(m > n)-dimensional Bakry-émery curvature is bounded from below by
-\fracm-1m-2l1(M){-\frac{m-1}{m-2}\lambda_1(M)}, then M splits isometrically as R × N whenever it has two ends with infinite weighted volume, here N is an (n − 1)-dimensional compact manifold. 相似文献
10.
For an arbitrary n-dimensional Riemannian manifold N and an integer m ∈ {1,…,n−1} a covariant derivative
on the Grassmann bundle ^ := Gm(T N) is introduced which has the property that an m-dimensional submanifold M ⊂ N has parallel second fundamental form if and only if its Gauss map M → ^ is affine. (For N Rn this result was already obtained by J. Vilms in 1972.) By means of this relation a generalization of Cartan's theorem on
the total geodesy of a geodesic umbrella can be derived: Suppose, initial data (p,W,b) prescribing a tangent space W ∈ Gm(TpN) and a second fundamental form b at p ∈ N are given; for these data we construct an m-dimensional ‘umbrella’ M = M(p,W,b) ⊂ N the rays of which are helical arcs of N; moreover, we present tensorial conditions (not involving
) which guarantee that the umbrella M has parallel second fundamental form. These conditions are as well necessary, and locally every submanifold with parallel
second fundamental form can be obtained in this way.
Mathematics Subject Classifications (2000): 53B25, 53B20, 53B21. 相似文献
11.
Lin-Feng Wang 《Annals of Global Analysis and Geometry》2010,37(4):393-402
Let M be an n-dimensional complete non-compact Riemannian manifold, dμ = e
h
(x)dV(x) be the weighted measure and
\trianglem{\triangle_{\mu}} be the weighted Laplacian. In this article, we prove that when the m-dimensional Bakry–émery curvature is bounded from below by Ric
m
≥ −(m − 1)K, K ≥ 0, then the bottom of the Lm2{{\rm L}_{\mu}^2} spectrum λ1(M) is bounded by
l1(M) £ \frac(m-1)2K4,\lambda_1(M) \le \frac{(m-1)^2K}{4}, 相似文献
12.
Dejan Kolarič 《Journal d'Analyse Mathématique》2009,107(1):239-250
We investigate the notion of CR transversality of a generic holomorphic map f: ℂ
n
→ ℂ
m
to a smooth CR submanifold M of ℂ
m
. We construct a stratification of the set of non-CR transversal points in the preimage M′ = f
−1 (M) by smooth submanifolds, consisting of points where the CR dimension of M′ is constant. We show the existence of a Whitney stratification for sets which are locally diffeomorphic to the product of
an open set and an analytic set.
Work on this paper was supported by ARRS, Republic of Slovenia. 相似文献
13.
Yong Seung CHO Myung Im LIM 《数学学报(英文版)》2006,22(1):115-122
Let (M, ω) be a closed symplectic 2n-dimensional manifold. Donaldson in his paper showed that there exist 2m-dimensional symplectie submanifolds (V^2m,ω) of (M,ω), 1 ≤m ≤ n - 1, with (m - 1)-equivalent inclusions. On the basis of this fact we obtain isomorphic relations between kernel of Lefschetz map of M and kernels of Lefschetz maps of Donaldson submanifolds V^2m, 2 ≤ m ≤ n - 1. Then, using this relation, we show that the flux group of M is discrete if the action of π1 (M) on π2(M) is trivial and there exists a retraction r : M→ V, where V is a 4-dimensional Donaldson submanifold. And, in the symplectically aspherical case, we investigate the flux groups of the manifolds. 相似文献
14.
M. Zippin 《Israel Journal of Mathematics》1981,39(4):349-358
It is proved that there exists a positive function Φ(∈) defined for sufficiently small ∈ 〉 0 and satisfying limt→0 Φ(∈) =0 such that for any integersn 〉>0, ifQ is a projection ofl
1
n
onto ak-dimensional subspaceE with ‖|Q‖|≦1+∈ then there is an integerh〉=k(1−Φ(∈)) and anh-dimensional subspaceF ofE withd(F,l
1
h
) 〈= 1+Φ (∈) whered(X, Y) denotes the Banach-Mazur distance between the Banach spacesX andY. Moreover, there is a projectionP ofl
1
n
ontoF with ‖|P‖| ≦1+Φ(∈).
Author was partially supported by the N.S.F. Grant MCS 79-03042. 相似文献
15.
In this paper we study central extensions of the identity component G of the Lie group C
∞
(M,K) of smooth maps from a compact manifold M into a Lie group K which might be infinite-dimensional. We restrict our attention to Lie algebra cocycles of the form ω(ξ,η)=[κ(ξ,dη)], where κ:𝔨×𝔨→Y is a symmetric invariant bilinear map on the Lie algebra 𝔨 of K and the values of ω lie in Ω1(M,Y)/dC
∞
(M,Y). For such cocycles we show that a corresponding central Lie group extension exists if and only if this is the case for M=𝕊1. If K is finite-dimensional semisimple, this implies the existence of a universal central Lie group extension of G. The groups Diff(M) and C
∞
(M,K) act naturally on G by automorphisms. We also show that these smooth actions can be lifted to smooth actions on the central extension if it also is a central extension of the universal covering group G˜ of G.
Received: 11 April 2002 / Revised version: 28 August 2002 /
Published online: 28 March 2003 相似文献
16.
17.
R. A. McCoy 《Mathematica Slovaca》2010,60(4):541-570
We introduce a lower semicontinuous analog, L
−(X), of the well-studied space of upper semicontinuous set-valued maps with nonempty compact interval images. Because the elements
of L
−(X) contain continuous selections, the space C(X) of real-valued continuous functions on X can be used to establish properties of L
−(X), such as the two interrelated main theorems. The first of these theorems, the Extension Theorem, is proved in this Part
I. The Extension Theorem says that for binormal spaces X and Y, every bimonotone homeomorphism between C(X) and C(Y) can be extended to an ordered homeomorphism between L
−(X) and L
−(Y). The second main theorem, the Factorization Theorem, is proved in Part II. The Factorization Theorem says that for binormal
spaces X and Y, every ordered homeomorphism between L
−(X) and L
−(Y) can be characterized by a unique factorization. 相似文献
18.
Studying the condition \({h(FX,Y)-h(X,FY)=g(FX,Y)\eta, 0\ne\eta\in T^\perp(M)}\) on the almost contact structure F and on the second fundamental form h of n-dimensional real submanifolds M of complex hyperbolic space \({\mathbb {CH}^{\frac{n+p}{2}}}\) when their maximal holomorphic tangent subspace is (n ? 1)-dimensional, we obtain the complete classification of such submanifolds M and we characterize certain model spaces in complex hyperbolic space. 相似文献
19.
Let X be a normed space that satisfies the Johnson–Lindenstrauss lemma (J–L lemma, in short) in the sense that for any integer
n and any x
1,…,x
n
∈X, there exists a linear mapping L:X→F, where F⊆X is a linear subspace of dimension O(log n), such that ‖x
i
−x
j
‖≤‖L(x
i
)−L(x
j
)‖≤O(1)⋅‖x
i
−x
j
‖ for all i,j∈{1,…,n}. We show that this implies that X is almost Euclidean in the following sense: Every n-dimensional subspace of X embeds into Hilbert space with distortion
22O(log*n)2^{2^{O(\log^{*}n)}}
. On the other hand, we show that there exists a normed space Y which satisfies the J–L lemma, but for every n, there exists an n-dimensional subspace E
n
⊆Y whose Euclidean distortion is at least 2Ω(α(n)), where α is the inverse Ackermann function. 相似文献
20.
A. L. Yakymiv 《Mathematical Notes》1995,58(5):1227-1230
Conditions on the distributions of two independent nonnegative random variablesX andY are given for the sumX+Y to have a subexponential distribution, i.e., (1−F
(2*)(t))/(1−F(t)) → 2 ast → +∞, whereF(t)=P{X+Y≤t} andF
(2*)(t) is the convolution ofF(t) with itself.
Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 778–781, November, 1995. 相似文献
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