Graphlike Manifolds with Contraction △×△

Ｇｒａｐｈｌｉｋｅ　Ｍａｎｉｆｏｌｄｓ　ｗｉｔｈ　Ｃｏｎｔｒａｃｔｉｏｎ　△×△ＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓｗｉｔｈＣｏｎｔｒａｃｔｉｏｎ△×△￥ＬｉｕＹａｘｉｎｇ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＨｅｎａｎＵｎｉｖｅｒｓｉｌｙ，Ｋａｉｆｅｎｇ，４...     

Graphlike Manifolds with Contraction ×

Ｇｒａｐｈｌｉｋｅ　Ｍａｎｉｆｏｌｄｓ　ｗｉｔｈ　Ｃｏｎｔｒａｃｔｉｏｎ　×ＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓｗｉｔｈＣｏｎｔｒａｃｔｉｏｎ×￥ＬｉｕＹａｘｉｎｇ；ＬｉＱｉｓｈｅｎｇ（Ｄｅｐｔ．ｏｆＭａｔｈ．ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，...     

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...     

On Graphlike Manifolds with Contraction

ＯｎＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓｗｉｔｈＣｏｎｔｒａｃｔｉｏｎＹｕａｎＦｕｙｏｎｇ（袁夫永）（ＵｎｉｖｅｒｓｉｔｙｏｆｓｔａｆｆａｎｄＷｏｒｋｅｒｓｏｆＡｇｒｉｃｕｌｔｕｒｅＲｅｃｌａｍａｔｉｏｎ）ＬｉｕＹａｘｉｎｇ（刘亚星）（Ｄｅｐａｒｔ...     

Graphlike Manifolds

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

Covering Spaces of Graphlike Manifolds

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

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…     

Graphlike Manifolds with the Type of the 1—skeleton of a 4—simplex

ＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓｗｉｔｈｔｈｅＴｙｐｅｏｆｔｈｅ１－ｓｋｅｌｅｔｏｎｏｆａ４－ｓｉｍｐｌｅｘＧｕｏＴｕｏｙｉｎｇ（ＨｕａｚｈｏｎｇＮａｒｍａｌＵｎｉｖｅｒｓｄｙ，Ｗｕｈａｎ，Ｃｈｉｎａ）（郭驼英）ｈＴｈｅｃｏｎｃｅｐｔｏｆｇｒａｐ...     

Graphlike Manifold with Torus as Bockstein

ＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｗｉｔｈＴｏｒｕｓａｓＢｏｃｋｓｔｅｉｎ￥ＬｉｕＹａｘｉｎｓ（ＵｎｉｗｒｓｉｔｙＯｆＨｅｌｅｎ，Ｋａｉｆｍｇ，４７５００１）（刘亚星）ＳｉｎｃｅａＨｏｍｅｍｏｒｐｈｉｓｍｆｒｏｍａＴｏｒｎｓｔｏａＴｏｒｎｓｉｓｄｅｔ...     

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 .     

Menger (Nöbeling) 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 . (Received 30 August 1999; in revised form 7 December 1999)     

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.     

Calabi–Yau Manifolds with Affine Structures

Mathematical Notes -     

Complete Open Manifolds with Nonnegative Ricci Curvature

In this paper, we study complete open manifolds with nonnegative Ricci curvature and injectivity radius bounded from below. We find that this kind of manifolds are diffeomorphic to a Euclidean space when certain distance functions satisfy a reasonable condition.     

H′-splittings of Seifert Manifolds with Boundary

Acta Mathematica Sinica, English Series - It is known that each compact connected orientable 3-manifold M with boundary admits an H′-splitting H1 ∪FH2, where F is a compact connected...     

A metrizable X with Cp(X) not homeomorphic to Cp(X) × Cp(X)

We give an example of an infinite metrizable space X such that the space C_p(X), of continuous real-valued functions on X endowed with the pointwise topology, is not homeomorphic to its own square C_p(X) × C_p(X). The space X is a zero-dimensional subspace of the real line. Our result answers a long-standing open question in the theory of function spaces posed by A. V. Arhangel’skii.     

On Some Total Chromatic Number ofOuterplanar Graphs with △(G) =6

ＯｎＳｏｍｅＴｏｔａｌＣｈｒｏｍａｔｉｃＮｕｍｂｅｒｏｆＯｕｔｅｒｐｌａｎａｒＧｒａｐｈｓｗｉｔｈ△（Ｇ）＝６￥ＺｈａｎｇＺｈｏｎｇｆｕ；ＬｕＸｉｎｚｈｏｎｇ；ＨａｎＪｉｎｃａｎｇ；ＬｉｎＫｅｒｏｎｇ（ＬａｎｚｈｏｕＲａｉｌｗａｙＩｎｓｔｉｔｕｔｅ，...