形式Generic流形的型

本文讨论形式Generic流形上的型．利用加权坐标系先对齐权流形给出计算型的一般步骤并把结 果推广到一般的形式Generic流形．     

Khler流形上的不变形式和积分不变量

用现代微分几何理论和高等微积分把Poincaré和Cartan_Poincaré积分不变量的重要思想和结果以及E.Cartan在经典力学中首先建立的积分不变量和不变形式的关系推广到Kahler流形上的Hamilton力学中去,得到相应的更广泛的结果.     

K(a)hler流形上的不变形式和积分不变量

用现代微分几何理论和高等微积分把Poincare和Cartan-Poincare积分不变量的晕要思想和结果以及E．Cartan在经典力学中首先建立的积分不变量和不变形式的关系推广到Kahler流形上的Hamilton力学中去，得到相应的更广泛的结果．     

黎曼流形上共形killing P—形式的对偶性

H.Yanamoto 在[2],[3]中有一猜想:对于任何黎曼流形 M~n,共形 Killingp-形式 u 的对偶*u 还是共形 Killing 形式。当 n=3时,这一结论的正确性由[3]给出.本文证明了对任何高维流形,结论都正确.     

复空间形式中具有共形MASLOV形式的拉格朗日子流形的一些例子

该文从实空间形式到复空间形式拉格朗日等距浸入中找到了一些非平凡的具有共形Maslov形式的拉格朗日子流形.     

Kaehler流形上的Hamilton力学

利用力学原理、现在微分几何理论和高等微积分把Hamihon力学推广至Kaehler流形上，建立Kaehler流形上Hamihon力学，并得到Hamilton向量场、Hamihon方程等复的数学形式．     

Kahler流形上的Lagrange向量场*

本文中。我们讨论K?hler流形上的Lagrange向量场,并用它来描述和解决Khler流形上的Newton力学和Lagrange力学中的一些问题。     

对偶扩张代数的分裂挠理论与Generic模

设A是一个有限维代数,R是A的对偶扩张代数.MA是一个A-模.给定一个倾斜R-模M(○)AR,我们知道MA一定是一个倾斜A-模.设(TM(○)AR,FM(○)AR)与(TM,FM)是分别由M (○)AR和MR导出的挠理论.本文讨论挠理论的分裂性以及Generic A-模与Generic R-模之间的关系。     

平凡扩张代数的Generic模

设A为代数闭域上的有限维代数.一个无限维不可分解A-模M称为Gen-eric模意指M作为它自同态环上的模是有限长度的.设R=ADA是A的平凡扩张代数.通过ModA与ModR之间的某些函子由Generic A-模构造出了Generic R-模.同时还证明了:当A为Tame遗传代数时,R有且仅有两个Generic模.     

PLEMELJ FORMULA OF CAUCHY TYPE INTEGRAL ON STEIN MANIFOLDS

Let D be a bounded domain with piecewise C(1) smooth orientable boundary on Stein manifolds, and let Φ(z) be a Cauchy type integral with Bochner-Martinelli kernel Ω(ψv, -S, S) and Holder continuous density function ψ(ζ), the authors define a solid angular coefficient α(t) at the point t ∈(e)D, prove that there exist the interior and outer limit values Φ± (t) under the meaning of the Cauchy principal value, and obtain the more general Plemelj formula and jump formula.     

GENERIC WARPED PRODUCT SUBMANIFOLDS OF LOCALLY CONFORMAL KEAHLER MANIFOLDS

Warped product manifolds are known to have applications in physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star （cf. [9]）. The studies on warped product manifolds with extrinsic geometric point of view were intensified after the B.Y. Chen＇s work on CR-warped product submanifolds of Kaehler manifolds （cf. [6], [7]）. Later on, similar studies were carried out in the setting of 1.c.K. manifolds and nearly Kaehler manifolds （el. [3], [11]）. In the present article, we investigate a larger class of warped product submanifolds of 1.c.K. manifolds, ensure their existence by constructing an example of such manifolds and obtain some important properties of these submanifolds. With regard to the CR-warped product submanifold, a special case of generic warped product submanifolds, we obtain a characterization under which a CR-submanifold is reducesd to a CR-warped product submanifold.     

WEAK TYPE(1,1)BOUNDEDNESS OF RIESZ TRANSFORM ON POSITIVELY CURVED MANIFOLDS

For complete Riemannian manifold M,it is proved that▽(-△)~(-1/2) is boundedfrom L~2(M)to weak-L~1(M)if Ric(M)≥0.     

关于稳定流形的扰动

本文中,M~n 普遍表一紧致的 n 维 C~∞ Riemann 流形,n≧2,(?)(M~n)表 M~n 上所有 C~1 常微系统作成的线性空间.如通常,后者赋以 C~1模‖o‖_1成为一 Banach 空间.任给一系统 S∈(?)(M~n).考虑 S 的一条双曲轨道.这等价于说这轨道在|M~n 中的闭包为 S 的双曲集,特别地,它可以是 S 的双曲奇点或双曲周期轨道.问题.设 S 过一点 c∈M~n 的轨道的 ω-极限集合г_c 与它的一条双曲轨道 P 相交.     

关于凸算子的广义Frechet可微性

本文得到如下结果：设F为从自反的Banaeh空间层到Banaeh格空间X的育有界凸算子，假若(i)X与X^*皆弱紧的区间；(ii)X有范紧区间，则F在层的某个稠子集Gδ的每一点都是Frechet可微的，推广了实值凸函数的有关结论．     

EXCESS FUNCTIONS OF RAYS ON COMPLETE NONCOMPACT MANIFOLDS

This paper gives an estimate of excess functions of rays on complete noncompact manifolds. By using this estimation, the authors can get the results in [3] as corollaries, which asserts that a complete manifold is diffeomorphic to R^n under some curvature and pinching conditions. At last, they obtain a refinement of them with extra Ricci condition.     

ON DOUBLY WARPED PRODUCT OF COMPLEX FINSLER MANIFOLDS

Let(M_1,F_1) and(M_2,F_2) be two strongly pseudoconvex complex Finsler manifolds.The doubly wraped product complex Finsler manifold(f_2M_1×f_1 M_2,F) of(M_1,F_1)and(M_2,F_2) is the product manifold M_1×M_2 endowed with the warped product complex Finsler metric F~2 =f_2~2 F_1~2 + f_1~2F_2~2,where f_1 and f_2 are positive smooth functions on M_1 and M2,respectively.In this paper,the most often used complex Finsler connections,holomorphic curvature,Ricci scalar curvature,and real geodesics of the DWP-complex Finsler manifold are derived in terms of the corresponding objects of its components.Necessary and sufficient conditions for the DWP-complex Finsler manifold to be Kahler Finsler(resp.,weakly Kahler Finsler,complex Berwald,weakly complex Berwald,complex Landsberg) manifold are obtained,respectively.It is proved that if(M_1,F_1) and(M_2,F_2) are projectively flat,then the DWP-complex Finsler manifold is projectively flat if and only if f_1 and f_2 are positive constants.     

UNIFORM ESTIMATES OF SOLUTIONS OF δ^--EQUATION ON STEIN MANIFOLDS

By means of the Hermitian metric and Chern connection, Qiu [4] obtained the Koppelman-Leray-Norguet formula for （p, q） differential forms on an open set with C^1 piecewise smooth boundary on a Stein manifold, and under suitable conditions gave the solutions of δ^--equation on a Stein manifold. In this article, using the method of Range and Siu [5], under suitable conditions, the authors complicatedly calculate to give the uniform estimates of solutions of δ^--equation for （p, q） differential forms on a Stein manifold.     

具非正则奇异性的偏微分方程的形式解（Ⅱ）

本文研究了具非正则奇异性的一阶全特征型偏微分方程的形式幂级数解.利用待定系数法证明了形式幂级数解的存在唯一性,并给出了其Gevrey类指标的计算公式.