Menger (N?beling) Manifolds versus Hilbert Cube (Space) Manifolds – A Categorical Comparison

 We show that the n-homotopy category of connected (n+1)-dimensional Menger manifolds is isomorphic to the homotopy category of connected Hilbert cube manifolds whose k-dimensional homotopy groups are trivial for each .     

Sasakian Submanifolds of Kaehlerian Manifolds(Ⅱ)

In this paper,it is proved that the Sasakian anti-holomorphic submanifolds of a Kaehlerian manifold is characterized by D-totally umbilical,and some curvature properties of the CR-submanifolds are ohtained.     

Graphlike Manifolds with Contraction △×△(Correction)

ＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓｗｉｔｈＣｏｎｔｒａｃｔｉｏｎ△×△（Ｃｏｒｒｅｃｔｉｏｎ）ＬｉｕＹａｘｉｎｇ（刘亚星）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉｆｅｎｇ，４７５００１）ＣｏｎｖｅｎｔｉｏｎＦｏｒｂｒｅｖｉ...     

Graphlike Manifolds

ＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓ￥ＬｉｕＹａｘｉｎｇ；ＬｉＱｉｓｈｅｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉｆｅｎｇ４７５００１，ＰＲＣ）Ａｂｓｔｒａｃｔ：Ｔｈｅｄｉｓｃｏｖｅｒｙｏｆｍａｎｉｆ...     

2-Harmonic Maps Between Riemannian Manifolds and Conservation Laws( Ⅰ )

As a generalization of harmonic maps,J. Eells and L.Lemaire present asuggestion of polyharmonic map of order κ,f: M→N,between Riemannianmanifolds which is the critical point critical point of the generalized k-energy functional, ifM is compact,     

2-Harmonic Maps Between Riemannian Manifolds and Conservation Laws (Ⅱ)

For harmonic map f: M→N,P.Baird and J. Eells have successfully foundout its stress-energy tensor S_f=e(f)g- f*h,which is called 1-stress-energy tensorin order to differ from what we’ll develop later.In view of the original defini-tion of 2-harmonic maps,people would ask what is the associated 2-stress-energytensor and the second conservation law of 2—harmonic maps.     

An Application of Machine Computation for Studying Graphlike Manifolds (Ⅱ)

51.IntroductionIntheirpaperL2j,LiuYaxingandLiQishengintroducedtheconceptofthegraphlikemanifolds.Slncegraphlikenlalifoldscanbe1ookeduponasgenera1izat1onofgraphsandcontalnthetorusandtheKleinbott1easspecialcases,theymakeupaimportantclassoftopologicalmanifolds.Thetopicabouttopologlcclassificat1onofgraphlikemanifoldswasresearchedln[2j,L4j,L5j,L6jand[7j.There,calculatingofhomeomorphicclassesisonthebas1softhefo1low1ngs:1.isomorphicgraphscanbcregardedasthesamecontraction;2.thetwistoperationpreserv…     

Generalized Contact Manifolds

ＧｅｎｅｒａｌｉｚｅｄＣｏｎｔａｃｔＭａｎｉｆｏｌｄｓＸｕＸｕｆｅｎｇＳｕｎＺｈｅｎｚｕ（ＸｕｚｈｏｕＮｏｒｍａｌＣｏｌｌｅｇｅ）（ＺｈｅｎｇｚｈｏｕＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：ＷｅｓｔｕｄｙａＲｉｅｍａｎｎｉａｎｍａｎｉｆｏｌｄｓＭｗｉ...     

Parameter Dependence of Stable Manifolds for Nonuniform (μ, ν)-dichotomies

We construct stable invariant manifolds for semiflows generated by the nonlinear impulsive differential equation with parameters x'= A(t)x + f(t, x, λ), t≠τi and x(τ+i) = Bix(τi) + gi(x(τi), λ), i ∈ N in Banach spaces, assuming that the linear impulsive differential equation x'= A(t)x, t≠τi and x(τ+i) = Bix(τi), i ∈ N admits a nonuniform (μ, ν)-dichotomy. It is shown that the stable invariant manifolds are Lipschitz continuous in the parameter λ and the initial values provided that the nonlinear perturbations f, g are sufficiently small Lipschitz perturbations.     

Holomorphic Maps from Sasakian Manifolds into K¨ahler Manifolds

The authors consider ±(Φ, J)-holomorphic maps from Sasakian manifolds into Ka¨hler manifolds, which can be seen as counterparts of holomorphic maps in Ka¨hler geometry. It is proved that those maps must be harmonic and basic. Then a Schwarz lemma for those maps is obtained. On the other hand, an invariant in its basic homotopic class is obtained. Moreover, the invariant is just held in the class of basic maps.     

Boundability of Open Manifolds

An open manifold in question is assumed to bea noncompact manifold with compact boundary (probably empty). Let M be a connected open n-dimensional smooth manifold. Take the one-point-compactification of M, it will be denoted by M=M∪{*}, where * is the infinite point. Since M has countable basis, M is metrizable and {*} is a closed subset and a G_δset. By Urysohn lemma, there exists a continuous function f:→[O,1] with f~-1(O)=M and f~-1(1)=*.Choose a sui-     

On Interposition in Manifolds

Let M be a C~∞-manifold, dim(M)= m, N a regular neat submanifold of M, dim(N) =n相似文献   

Covering Spaces of Graphlike Manifolds

ＣｏｖｅｒｉｎｇＳｐａｃｅｓｏｆＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓ￥ＬｕｉＹａｘｉｎｇ（ＵｎｉｖｅｒｓｉｔｙｏｆＨｅｎａｎ，Ｋａｉｆｅｎｇ，４７５００１）（刘亚星）ＬｅｔＭｂｅｔｈｅｇｒａｐｈｌｉｋｅｍａｎｉｆｏｌｄｏｂｔａｉｎｅｄｂｙｉｄｅｎｔｉ...     

Isolation Phenomena for Einstein Manifolds

Let M be a compact n-dimensional Einstein manifold without boundary. Denoteby R_(ijkl) the Riemannian curvature tensor with respect to a local orthonormal framefield. Tbe Ricci curvature tensor is given by     

Graphlike Manifolds with Contraction 

ＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓｗｉｔｈＣｏｎｔｒａｃｔｉｏｎ ＬｉｕＸｉａｏｚｈｅｎ（刘晓真）Ｇｒａｐｈｌｉｋｅ　Ｍａｎｉｆｏｌｄｓ　ｗｉｔｈ　Ｃｏｎｔｒａｃｔｉｏｎ ￥ＬｉｕＸｉａｏｚｈｅｎ（ＨｅｎａｎＩｎｓｔｉｔｕｔｅｏｆＦｉｎａｎｃｅａｎ...     

Graphlike Manifolds with Contraction 

Ｇｒａｐｈｌｉｋｅ　Ｍａｎｉｆｏｌｄｓ　ｗｉｔｈ　Ｃｏｎｔｒａｃｔｉｏｎ　ＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓｗｉｔｈＣｏｎｔｒａｃｔｉｏｎＬｉｕＸｉａｏｚｈｅｎ（ＨｅｎａｎＩｎｓｔｉｔｕｔｅｏｆＦｉｎａｎｃｅａｎｄＥｃｏｎｏｍｉｃｓ，Ｚｈｅｎｇｚ...     

Problems Concerning Embeddings of Manifolds

Very little is known in general about estimating the smallest integer l such that a manifold Mn emheds in Rn+k +l if it immerses in Rn+k. Indeed there are relatively few examples where k and l can be estimated accurately. There are old examples for which l is known to be arbitrarily Iarge; for those examples l can grow like logn and there are recent examples where l can grow linearly with n. The main difficulty in resolving questions of this kind is that the only general methods known for proving non-embedding and non-immersion results involve doing calculations with characteristic classes and the estimates that they give are very similar for the two problems. In this paper an account is given of various methods that can be used to study examples.     

Computing Degree of Maps Between Manifolds

We determine the degrees of maps between two given closed （n-1）-connected 2n-mamifolds when n ≡ 1 （mod 8）.     

A Class of Homogeneous Einstein Manifolds

A Riemannian manifold (M, g) is called Einstein manifold if its Ricci tensor satisfies r = c·g for some constant c. General existence results are hard to obtain, e.g., it is as yet unknown whether every compact manifold admits an Einstein metric. A natural approach is to impose additional homogeneous assumptions. M. Y. Wang and W. Ziller have got some results on compact homogeneous space G/H. They investigate standard homogeneous metrics, the metric induced by Killing form on G/H, and get some classification results. In this paper some more general homogeneous metrics on some homogeneous space G/H are studies, and a necessary and sufficient condition for this metric to be Einstein is given. The authors also give some examples of Einstein manifolds with non-standard homogeneous metrics.