Graphlike Manifolds with Contraction 

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

On Graphlike Manifolds with Contraction

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

Graphlike Manifolds with Contraction ×

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

Graphlike Manifolds with Contraction △×△

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

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...     

Covering Spaces of Graphlike Manifolds

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

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...     

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…     

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...     

K?hler Manifolds with Almost Non-negative Ricci Curvature

Compact Kähler manifolds with semi-positive Ricci curvature have been investigated by various authors. From Peternell’s work, if M is a compact Kähler n-manifold with semi-positive Ricci curvature and finite fundamental group, then the universal cover has a decomposition \( \ifmmode\expandafter\tilde\else\expandafter\~\fi{M} \cong X_{1} \times \cdots \times X_{m} \), where X _j is a Calabi-Yau manifold, or a hyperKähler manifold, or X _j satisfies H ⁰(X _j , Ω ^p ) = 0. The purpose of this paper is to generalize this theorem to almost non-negative Ricci curvature Kähler manifolds by using the Gromov-Hausdorff convergence. Let M be a compact complex n-manifold with non-vanishing Euler number. If for any ∈ > 0, there exists a Kähler structure (J _∈, g _∈) on M such that the volume \({\text{Vol}}_{{g_{ \in } }} {\left( M \right)} < V\), the sectional curvature |K(g _∈)| < Λ², and the Ricci-tensor Ric(g _∈)> ?∈g _∈, where V and Λ are two constants independent of ∈. Then the fundamental group of M is finite, and M is diffeomorphic to a complex manifold X such that the universal covering of X has a decomposition, \( \ifmmode\expandafter\tilde\else\expandafter\~\fi{X} \cong X_{1} \times \cdots \times X_{s} \), where X _i is a Calabi-Yau manifold, or a hyperKähler manifold, or X _i satisfies H ⁰(X _i , Ω ^p ) = {0}, p > 0.     

Quasi—conformally Flat Manifolds with Constant Scalar Curvature

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＭｂｅａｎｎ－ｄｉｍｅｎｓｉｏｎａｌｃｏｎｆｏｒｍａｌｌｙｆｌａｔｍａｎｉｆｏｌｄｗｉｔｈｃｏｎｓｔａｎｔｓｃａｌａｒｃｕｒｖａｔｕｒｅρ（ｎ≥３）．ＷｈｅｎｔｈｅＲｉｃｃｉｃｕｒｖａｔｕｒｅＳｏｆＭｉｓｏｆｂｏｕｎｄｅｄｂｅｌｏｗａｎｄｙＳｙ２＜ρ２／（ｎ－１），Ｇｏｌｄ－ｂｅｒｇｐｒｏｖｅｄｔｈａｔＭｉｓｏｆｃｏｎｓｔａｎｔｃｕｒｖａｔｕｒｅ［１］．ＷｈｅｎＭｉｓａｃｏｍｐａｃｔｍａｎｉｆｏｌｄｗｉｔｈｐｏｓｉｔｉｖｅＲｉｃｃｉｃｕｒｖａｔｕｒｅ，ＷｕＢ…     

Holomorphic Vector Bundle on Hopf Manifolds with Abelian Fundamental Groups

Let X be a Hopf manifolds with an Abelian fundamental group.E is a holomorphic vectorbundle of rank r with trivial pull-back to W=C~n-{0}.We prove the existence of a non-vanishingsection of L(?)E for some line bundle on X and study the vector bundles filtration structure of E.These generalize the results of D.Mall about structure theorem of such a vector bundle E.     

Generalized Contact Manifolds

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

Compact Almost Kähler Manifolds with Divergence-Free Weyl Conformal Tensor

We prove that a compact almost Kähler manifold satisfying that a certain part of thedivergence W of the Weyl conformal tensor W vanishes isKähler.