Compact Kähler manifolds with elliptic homotopy type

Simply connected compact Kähler manifolds of dimension up to three with elliptic homotopy type are characterized in terms of their Hodge diamonds. For surfaces there are only two possibilities, namely h1,1?2 with hp,q=0 for p≠q. For threefolds, there are three possibilities, namely h1,1?3 with hp,q=0 for p≠q. This characterization in terms of the Hodge diamonds is applied to explicitly classify the simply connected Kähler surfaces and Fano threefolds with elliptic homotopy type.     

丛上的相交数与Euler数

本文主要研究了带边流形上丛截面的相交数．应用作倍流形上的向量场的延拓，我们得到了带边流形上的Euler数用相交数的表示．     

关于Finsler曲面的几何和拓扑

本文在Ｆｉｎｓｌｅｒ曲面上定义了一个新的不变量Ｈ。该不变量等于零刻画了Ｒｉｅｍａｎｎ流形。文章给出了Ｈ的一个上界并且构造了Ｈ为常值的非Ｒｉｅｍａｎｎ的Ｆｉｎｓｌｅｒ曲面。此外，本文还推广了Ｌａｎｄｓｂｅｒｇ曲面的Ｇａｕｓ－Ｂｏｎｎｅｔ－Ｃｈｅｒｎ定理并分类了非正曲率的Ｆｉｎｓｌｅｒ曲面。     

二维紧致具有非正曲率Riemann流形Euler数的一个计算公式

设Ｍ是二维紧致、曲率Ｋ（Ｍ）≤０的Ｒｉｅｍａｎｎ流形．对任一ｘ　Ｍ,在Ｍ上类数≥３的点集非空且只有有限个点｛α１,α２,…;αｄ｝．用Ｋｊ表示αｊ的类数,即αｊ到ｘ的最短测地线的条数．那么,Ｍ的Ｅｕｌｅｒ数Ｘ（Ｍ）可以表示为：Ｘ（Ｍ）＝（ｄ＋１）＝Ｋｊ．如果Ｍ上类数２３的点只有一个,那么这个点是Ｍ上距离ｘ最远的点．     

凸体的弦幂积分公式

本文研究了高维欧氏空间中凸体的弦幂积分问题.利用积分的方法,获得了凸体弦幂积分的几个积分公式.     

一类反常积分的另解及推广

利用Euler公式、和差化积公式、换元积分法,对一道反常积分题给出三种新解法,并给出它的两个推广情形．     

Algorithms for finding proper essential surfaces in 3-manifolds

In this paper, we present an algorithm which, for a given compact orientable irreducible boundary irreducible 3-manifold M, verifies whether M contains an essential orientable surface (possibly, with boundary), whose genus is at most N. The algorithm is based on Haken’s theory of normal surfaces, and on a trick suggested by Jaco and consisting in estimating the mean length of boundary curves in an unknown essential surface of a given genus in the given manifold.     

Additivity for the parametrized topological Euler characteristic and Reidemeister torsion

Dwyer, Weiss, and Williams have recently defined the notions of the parametrized topological Euler characteristic and the parametrized topological Reidemeister torsion which are invariants of bundles of compact topological manifolds. We show that these invariants satisfy additivity formulas paralleling the additive properties of the classical Euler characteristic and the Reidemeister torsion of CW-complexes.     

Schrödinger operators on graphs and geometry I: Essentially bounded potentials

The inverse spectral problem for Schrödinger operators on finite compact metric graphs is investigated. The relations between the spectral asymptotics and geometric properties of the underlying graph are studied. It is proven that the Euler characteristic of the graph can be calculated from the spectrum of the Schrödinger operator in the case of essentially bounded real potentials and standard boundary conditions at the vertices. Several generalizations of the presented results are discussed.     

Collapses, products and LC manifolds

The quantum physicists Durhuus and Jonsson (1995) [9] introduced the class of “locally constructible” (LC) triangulated manifolds and showed that all the LC 2- and 3-manifolds are spheres. We show here that for each d>3 some LC d-manifolds are not spheres. We prove this result by studying how to collapse products of manifolds with one facet removed.     

重积分和线面积分中的一个典型题目

针对授课班级出错率较高的一道曲面积分题目,给出四种解法.分析出错的原因在于练习不够外,主要是对重积分概念理解不够透彻.     

Total coloring of graphs embedded in surfaces of nonnegative Euler characteristic

Let G be a graph which can be embedded in a surface of nonnegative Euler characteristic.In this paper,it is proved that the total chromatic number of G is △(G)+1 if △(G)9,where △(G)is the maximum degree of G.     

An Equivalent Flat Condition

We show that on an 8-dimensional manifold with Euler characteristic zero every semiflat metric must be flat.     

Euler求和公式的一种推广和应用

将只适用于有限区间上具有连续微商的函数的Eu ler求和公式推广到一般的连续函数,并应用此公式推出对于满足L ipsch itz条件的函数普通数值积分的梯形法、矩形法与S im pson法.     

THE INTEGRAL FORMULA ON COMPLEX SUBMANIFOLD AND APPLICATION

1IntroductionWeknowthateverysttrictlyconvexdomainwithC*-boundaryisastrictlypseudoconvexdomainwithCk-boundary,wherek21.AfteranappropriatelOcalchangeofholomorphiccoordinates,theconverseisalsotrue.LetDCC\"beastrictlypseudoconvexdomainwithCdboundary.MorepreciselyD={z6Cn:p(z)<0},wherepisaCdrealvaluedstrictlyplurisubharmonicfunctiononaneighborhoodreofD,andgradpfoonaD.SupposeFI,')Fmareholomorphicfunctionsonre,setWeassumez(FI,',Fm)meetsODtransversally.SetD=Z(FI,'tFm)nD.Let(EOD,thenf…