Blowing-ups and valuations on surfaces

In this paper, we show that all the nontrivial valuations on surfaces can be given by the infinite sequences of blowing-ups, and give the process of blowing-ups.     

全序幂等元剩余格

研究了全序幂等元剩余格,给出了全序幂等元剩余格的另一种新的构造方法,并且得到了这类剩余格的结构定理,推广了相关文献的结论．     

关于四元射影空间中的全实2-调和子流形

利用了活动标架法对四元射影空间QPnc中全实2-调和子流形进行了研究,获得了这类子流形成为全实极小子流形的刚性定理,推广了相关文献中的积分不等式．     

On the Bergman representative coordinates

We study the set where the so-called Bergman representative coordinates (or Bergman functions) form an immersion. We provide an estimate of the size of a maximal geodesic ball with respect to the Bergman metric contained in this set. By concrete examples we show that these estimates are the best possible.     

复空间形式中常数量曲率的完备全实伪脐子流形

设CNnc是具有常全纯截面曲率c(≤O)的复n维的复空间形式,Mn是CNnc中常数量曲率的完备全实伪脐子流形,R,‖h‖2分别表示Mn的标准数量曲率和第二基本形式模长的平方.假设R≥c/4.利用丘成桐的广义极大值原理和自伴随算子研究了关于‖h‖2的pinching问题,得到了两个Mn成为全测地或全脐的刚性定理.     

Maximal resolvability of totally bounded and ℵ0-bounded groups

The maximal resolvability of totally bounded groups (and, under the assumption that the generalized continuum hypothesis holds, of ₀-bounded groups) is proved.Translated fromMatematicheskie Zametki, Vol. 63, No. 4, pp. 593–598, April, 1998.This research was supported by the Russian Foundation for Basic Research under grant No. 94-01-01374.     

Quasi—Einstein Hypersurfaces in a Hyperbolic Space

§1.　IntroductionLetRijbethecomponentsofRiccitensorofann-dimensionalRiemannianmanifoldM.IfRij=Agij Bξiξj,　(i,j=1,2,…,n)(1.1)whereξisanunitvectorfield,thenMiscalledaquasi-EinsteinmanifoldanddenotedbyQE(ξ).Ifξisanisotropicvectorfield,thenMiscalledageneralizedquasi-Einsteinmanifold.Intheequality(1.1),AandBarescalarfunctions.WeknowQE(ξ)manifoldisEinsteinwhenB≡0.Especially,if〈ξ,ξ〉=e=±1,thenQE(ξ)iscalledanormalquasi-Einsteinmani-fold.Itiseasytoknowfrom[1]and[2]:Rij=R-Tn-1…     

Symplectic Matroids

A symplectic matroid is a collection B of k-element subsets of J = {1, 2, ..., n, 1*, 2*, ...; n*}, each of which contains not both of i and i* for every i n, and which has the additional property that for any linear ordering of J such that i j implies j* i* and i j* implies j i* for all i, j n, B has a member which dominates element-wise every other member of B. Symplectic matroids are a special case of Coxeter matroids, namely the case where the Coxeter group is the hyperoctahedral group, the group of symmetries of the n-cube. In this paper we develop the basic properties of symplectic matroids in a largely self-contained and elementary fashion. Many of these results are analogous to results for ordinary matroids (which are Coxeter matroids for the symmetric group), yet most are not generalizable to arbitrary Coxeter matroids. For example, representable symplectic matroids arise from totally isotropic subspaces of a symplectic space very similarly to the way in which representable ordinary matroids arise from a subspace of a vector space. We also examine Lagrangian matroids, which are the special case of symplectic matroids where k = n, and which are equivalent to Bouchet's symmetric matroids or 2-matroids.     

On Affine Geometry of Purley Real Submanifolds

We propose to study n-dimensional purely real submanifolds of the standard affine complex space Cⁿ from an affine point of view. Such submanifolds are naturally endowed with a unique transversal bundle. Fundamental theorems are given as well as a theorem of Cartan–Norden type. Examples illustrating particular affine properties of such submanifolds are provided.     

约束力学系统的联络及其运动方程的测地性质

用现代整体微分几何方法研究非定常约束力学系统运动方程的测地性质，得到非定常力学系统的动力学流关于１＿射丛上的联络具有测地性质的充分必要条件·非定常情形下的动力学流关于无挠率的联络总具有测地性质，因此任何非定常约束力学系统在外力作用下的运动总可以表示为关于１＿射丛上无挠率的动力学联络的测地运动，这与定常力学的情形有所区别·