类拟的Euler公式

经典的欧拉公式描述了两曲面交线的曲率和曲面的法曲率以及曲面夹角之间的关系。本文给出了R3中曲面的法曲率的欧拉公式的简单证明。并得到一个关于曲面交线曲率及曲面测地曲率的类似的欧拉公式。     

完备正曲率凯拉流形的体积增长与曲率衰减

在C~n上构造了一族全纯截曲率为正的凯拉度量,并证明所构造的度量具有如下性质：当测地距离ρ趋于无穷时,测地球的体积增长为O(■),而黎曼标量曲率的衰减为O(■),其中β≥0．     

关于Finsler流形中的距离函数与测地球

利用Finsler流形中的切曲率和旗曲率，研究了距离函数与测地球的凸性；指出了在单连通完备Minkowski空间中测地球正好是平面的一部分。     

完备正曲率凯拉流形的体积增长与曲率衰减

在Cn上构造了一族全纯截曲率为正的凯拉度量,并证明所构造的度量具有如下性质当测地距离ρ趋于无穷时,测地球的体积增长为O(ρ2(β+1)n/β+2),而黎曼标量曲率的衰减为O(ρ-2(β+1)β+2),其中β≥0.     

关于Finsler流形中的距离函数与测地球

利用 Finsler流形中的切曲率和旗曲率 ,研究了距离函数与测地球的凸性 ;指出了在单连通完备 Minkowski空间中测地球正好是平面的一部分     

CP~n 的完备全实具有平行中曲率向量的子流形

本文的目的在于给出一种方法,它可以看作通常的 Bochner 技巧的改进,据此我们证明了 CP~n 的完备全实具有平行中曲率向量和强正截曲率的 n 维子流形是全测地的.     

CP^n中具有平行中曲率向量的全实子流形

本文讨论复射影空间 CP~n 中的全实子流形 M 在什么条件下为全测地或全脐的问题,就具有平行中曲率向量的这种子流形,文中给出利用 M 的数量曲率满足不等式来判断的一些定理(见定理1—4)。     

完备Riemann流形之共轭点

本文证明了具非负曲率完备Ｒｉｅｍａｎｎ测地线为无共轭点测地线的充要条件；并由此证明了若该流形上的截面含有一无共轭点测地线的切向量，则其对应的截曲率为零．     

关于复射影空间的三维全实极小子流形

本文给出复射影空间中三维紧致全实极小子流形的Ricci曲率和数量曲率的鞭些拼挤定理.特别是证得:若M³是CP³的紧致全实极小子流形且它的Ricci曲率大于1/6,则M³是全测地的.     

关于四元射影空间的正曲率全复子流形

本文讨论四元射影空间的全复子流形，证明了四元射影空间的正截面曲率紧致全复子流形一定是全测地的。     

Two questions on the exterior geometry of the plücker embeddings of the Grassmann manifolds

The Plücker model of the Grassmann manifold G _p,p+q ⁺ is considered. The structure of intersections of G _p,p+q ⁺ with tangent spaces of G _p,p+q ⁺ regarded as subspaces of the ambient exterior algebra is described. An explicit formula for the second fundamental form of G _2,4 ⁺ as of a hypersurface in the five-dimensional sphere is given. The level sets of the normal curvature functions for this hypersurface are studied. Bibliography: 3 titles. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 246, 1997, pp. 5–12. Translated by N. Yu. Netsvetaev.     

Regular boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces

We consider coerciveness and Fredholmness of nonlocal boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces. In some special cases, the main coefficients of the boundary conditions may be bounded operators and not only complex numbers. Then, we prove an isomorphism, in particular, maximal L _p -regularity, of the problem with a linear parameter in the equation. In both cases, the boundary conditions may also contain unbounded operators in perturbation terms. Finally, application to regular nonlocal boundary value problems for elliptic equations of the second order in non-smooth domains are presented. Equations and boundary conditions may contain differential-integral parts. The spaces of solvability are Sobolev type spaces W _p,q ^2,2. The first author is a member of G.N.A.M.P.A. and the paper fits the 60% research program of G.N.A.M.P.A.-I.N.D.A.M.; The third author was supported by the Israel Ministry of Absorption.     

Complete and Stable O(p+1)×O(q+1)-Invariant Hypersurfaces with Zero Scalar Curvature in Euclidean Space ℝ p+q+2

We classify the zero scalar curvature O(p+1)×O(q+1)-invariant hypersurfaces in the euclidean space ℝ ^p+q+2, p,q > 1, analyzing whether they are embedded and stable. The Morse index of the complete hypersurfaces show the existence of embedded, complete and globally stable zero scalar curvature O(p+1)×O(q+1)-invariant hypersurfaces in ℝ ^p+q+2, p+q≥ 7, which are not homeomorphic to ℝ ^p+q+1. Such stable examples provide counter-examples to a Bernstein-type conjecture in the stable class, for immersions with zero scalar curvature. Mathematics Subject Classifications (2000): 53A10, 53C42,49005.     

Eine Spektralsequenz in der stetigen Kohomologietheorie topologischer Gruppen

Let H^*(G; M) be the continuous cohomology of a locally compact group G with coefficients in a topological RG-module M. If G operates without fixed points on a R-paracompact space X such that there is a slice through each point and X/G is R-paracompact, then there exists a spectral sequence converging to the equivariant cohomology H^*(X,G; M) of X with second term E₂ ^p.q?H^p(G; H^qX; M)) where the sheaf theoretical cohomology of X is suitable topologized. Several applications and a generalization to actions of G with non-empty fixed point sets are given.     

广义Campanato空间上粗糙核参数型Marcinkiewicz积分

作为一类Littlewood-Paley函数,μ_(Ω,b)~ρ(f)是带非齐次粗糙核的参数型Marcinkiewicz积分,其中粗糙核Ω∈L~q(S~(n-1))满足消失性和积分Dini连续,径向核b∈Δ_s(R~+)∩Θ_s(R~n),1q,s∞,复参数ρ具有正实部.仅在一点有限的假设下,该文建立了μ_(Ω,b)~ρ(f)在广义Campanato空间L~(p,φ)(R~n)上的存在性和有界性,本质地推进了众多的已有工作.     

Complete unital-derived arcs in the hall planes

We prove the existence of complete (q ² -q + 1)-arcs in each Hall plane of orderq ²,q ² > 9. Work performed under the auspicies of the G.N.S.A.G.A. of the C.N.R. (National Research Council) of Italy and supported by M.U.R.S.T. progetto “Strutture Geometriche Combinatoria e Loro Applicazioni”.     

单位球上小Bloch型空间之间的加权复合算子

对所有的0p、q∞,该文得到了Cn中单位球上小Bloch型空间β_0~p到β_0~q之间的加权复合算子T_ψ,φ为有界算子或紧算子的充要条件.     

Dedekind symbols with plus reciprocity laws

Dedekind symbols are generalizations of the classical Dedekind sums (symbols), and the symbols are determined uniquely by their reciprocity laws, up to an additive constant. For Dedekind symbols D and F, we can consider two kinds of reciprocity laws: D(p,q)−D(q,−p)=R(p,q) and F(p,q)+F(q,−p)=T(p,q). The first type, which we call minus reciprocity laws, have been studied extensively. On the contrary, the second type, which we call plus reciprocity laws, have not yet been investigated. In this note we study fundamental properties of Dedekind symbols with plus reciprocity law F(p,q)+F(q,−p)=T(p,q). We will see that there is a fundamental difference between Dedekind symbols with minus and plus reciprocity laws.     

由分数次导数所确定的L2(T)中的一元周期函数类在Lq(T)中的相对宽度

作者研究了相对宽度K_n(W₂^α(T), MW₂^β(T), L₂(T)), T=[0,2π], 确定了使等式K_n(W₂^α(T), MW₂^β(T), L₂(T))=d_n(W₂^α(T), L₂(T))成立的最小M值, 得到了相对宽度K_n(W₂^α(T), W₂^α(T), L_q(T))的渐近阶, 其中α≥β>0, 1≤q≤∞, K_n(., ., L_q(T)) 和 d_n(., L_q(T))分别表示Kolmogorov意义下L_q(T)尺度下的相对宽度和宽度, MW_p^α(T), 1≤ p≤∞, 表示有如下卷积表达式的2π 周期函数类, f(t)=c+(B_α* g)(t),c∈ R, B_α*g 表示 B_α 和g 的卷积, g∈L_p(T) 满足∫₀^2πg(τ)dτ=0 和||g||_p≤M, B_α∈ L₁(T) 有如下Fourier展开: B_α(t)=1/2π∑' _{k∈ Z}(ik)^-αe^ikt,∑^'表示去掉 k=0的项.     

Maximal characterizations of Herz type Hardy spaces on homogeneous groups

In this paper, the authors establish some characterizations of Herz-type Hardy spaces HKα,p q(G) and HKq,p q(G), where 1 ＜ q ＜∞, Q(1 - 1/q) ≤α＜∞, 0 ＜ p ＜∞ and G denotes a graded homogeneous Lie group.