共查询到19条相似文献,搜索用时 62 毫秒
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本文对三维Minkowski空间R^2,1中具有性质K-2mH m^2-ι^2=0或H=constant的类时曲面定义了一个Darboux线汇,同时得到了相应的Baecklund变换。 相似文献
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在利用高斯公式计算第二类曲面积分时 ,若曲面为非封闭曲面 ,此时添加辅助曲面时 ,要特别注意 ,要保证在封闭曲面及内部满足高斯公式的条件 ,稍有不慎就会得出错误的结果 .如下面这个例子 :例 算曲面积分 I = Σxdydz ydzdx zdxdy(x2 y2 z2 ) 3/2 ,其中Σ为曲面 1 -z5 =(x -2 ) 21 6 (y -1 ) 29(z≥ 0 )的上侧 .解 令 P =x(x2 y2 z2 ) 3/2 ,Q =y(x2 y2 z2 ) 3/2 ,R =z(x2 y2 z2 ) 3/2设Σ1是 xoy平面上由 (x -2 ) 21 6 (y -1 ) 29≤ 1所围部分的下侧 ,Ω是Σ与Σ1所围闭域 .∵ P x =-2 x2 y2 z2(x2 y2 z2… 相似文献
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张维Hao 《数学物理学报(A辑)》1992,12(2):136-139
设Ω是R~n(n≥2)中的单连通有界开集,其边界骪Ω是无限可微的封闭超曲面。设H(S)是Ω的平均曲率(n=2,H(s)是曲率)。假定s∈Ω,H(s)>0。记 则我们证明 ii)H_0/H_1≤(1-1/n)~2|Ω|/|Ω|~2 integral from n=Ω to (ds)/(H(s))~2, iii)|Ω|≤(1-1/n)integral from n=Ω to (ds)/H(s), 我们有如下未解决问题:是否成立不等式 相似文献
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高斯公式应用小议 总被引:1,自引:0,他引:1
在利用高斯公式计算曲面积分时 ,许多学生往往忽视了对定理条件的考察。比如 :同济四版《高等数学》下册总习题十的第 3 ( 4)题就是一例。例 1 :计算 ∑xdydz +ydzdx +zdxdy( x2 +y2 +z2 ) 3 ,其中 ∑:1 -z5=( x -2 ) 21 6+( y -1 ) 29( z≥ 0 )上侧。多数学生在利用高斯公式求解时 ,做法如下 :解 :令 P =x( x2 +y2 +z2 ) 3 ,Q =y( x2 +y2 +z2 ) 3 ,R =zx2 +y2 +z2 ) 3 ,补 ∑1:z =0 ( x -2 ) 21 6+( y -1 ) 29≤ 1 下侧。于是由高斯公式得 : ∑+ ∑ 1Pdydz +Qdzdx +Rdxdy = Ω P x+ Q y+ R z dv Ω0 dv =0 ,其中Ω为由 ∑ +∑1所围区… 相似文献
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R2,1中类时Weingarten曲面的Bcklund变换 总被引:1,自引:0,他引:1
本文利用平行变换,得到3维Minkowski空间R2,1中的K-2mH+m2-l2=0(H2>K,0≤m相似文献
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本文属于仿射微分几何。在3-维欧氏空间 E~3中,F.Scherk 定理告诉我们,极小平移曲面必需是平面或 Scherk 曲面az=1n(cos ax/cos ay),a=constant。在一般(n+1)维仿射空间 A~(n+1)中,仿射极小平移超曲面是什么曲面?本文得到了这种曲面共有两类的结果(见定理1)。当 n=2时,这就是引文[3]中的结果(见定理2)。 相似文献
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本文研究了 CPn中的弱等焦Hopf超曲面的分类,弱等焦超曲面首先是由滕楚莲与Thorbergsson在[13]中引入的.设M是CPn中的弱等焦Hopf超曲面,则M的不同焦半径的个数是2,4或6;并且当g=2或4时,M在CPn中是等参的;当g=6时,n=8,(M-)=π-1(M)与S7中的等参超曲面不Lie等价,此处π:S7→CP3是Hopf纤维化. 相似文献
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多元函数积分学的物理意义在解题中的应用 总被引:1,自引:0,他引:1
本文用高等数学知识和物理知识相结合 ,利用多元函数积分学的物理意义解决一类题目 ,显得相当简便。例 1 设 D是以点 O( 0 ,0 )、A( 1 ,2 )和 B( 2 ,1 )为顶点的三角形区域 ,求 Dxdxdy.解 直线 OA,OB和 AB的方程分别为y =2 x,y =12 x和 y =3 -x Dxdxdy = D1xdxdxy + D2xdxdy =∫10xdx∫2 xx/2dy +∫21xdx∫3- xx/2dy =32 . 本题若用形心公式则更为简便 :由形心公式 x= Dxdσ Ddσ得 , Dxdσ=x. Ddσ.形心横坐标为 :x=0 +1 +23 =1 ,此三角形的面积为 32 ,所以 Dxdxdy =32 .此法具有通用性 ,对于规则的形体都适用。例 2… 相似文献
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V. P. Gorokh 《Journal of Mathematical Sciences》1991,53(5):491-493
We prove that any piece of a space-like minimal surface of the form z=z(x, y), in the pseudo-Euclidean space E3,1 with line element dx2+dy2–dz2 has the greatest area among close space-like surfaces with the same boundary. For time-like surfaces the following assertion is proved. Let V2 be a time-like minimal surface in E3,1. Then for any domain on V2, there exists a smooth variation in the class of time-like surfaces with fixed boundary that increases the area, and there exists a smooth variation in the same class of surfaces that decreases the area.Translated from Ukrainskii Geometricheskii Sbornik, No. 33, pp. 41–45, 1990. 相似文献
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Gu Chaohao 《数学年刊B辑(英文版)》1994,15(4):385-400
COMPLETEEXTREMALSURFACESOFMIXEDTYPEIN3-DIMENSIONALMINKOWSKISPACE¥GUCHAOHAO(InstituteofMathematics,FudanUniversity,Shanghai200... 相似文献
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Space-like surfaces and time-like surfaces with zero mean curvature vector in oriented neutral 4-manifolds are isotropic and compatible with the orientations of the spaces if and only if their lifts to the space-like and the time-like twistor spaces respectively are horizontal. In neutral Kähler surfaces and paraKähler surfaces, complex curves and paracomplex curves respectively are such surfaces and characterized by one additional condition. In neutral 4-dimensional space forms, the holomorphic quartic differentials defined on such surfaces vanish. There exist time-like surfaces with zero mean curvature vector and zero holomorphic quartic differential which are not compatible with the orientations of the spaces and the conformal Gauss maps of time-like surfaces of Willmore type and their analogues give such surfaces. 相似文献
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We find all space-like loxodromes on rotational surfaces which have space-like meridians or time-like meridians, respectively by using a relevant Lorentzian angle in Minkowski 3-space. To understand loxodromes better, we draw some pictures of them via Mathematica computer program. 相似文献
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In this paper, infinitesimal deformations of time-like surfaces are investigated in Minkowski 3-space R^2,1. It is shown that some given deformations of the time-like surface can be described by 2 1 dimensional integrable systems. Moreover spectral parameters are introduced, and it is proved that deformation families are soliton surfaces‘ families. 相似文献
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本文研究了三维Minkowski空间中直线汇的一些性质,特别是关于类时线汇的性质.讨论了线汇基本元素的存在性,并证明了关于三维Minkowski空间中类时线汇的配分参数的一个结果,推广了苏步青1927年的—个成果. 相似文献
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Da Feng ZUO 《数学学报(英文版)》2006,22(4):1021-1026
In this paper we study Backlund transformations of time-like linear Weingarten surfaces with negative discriminant in Lorentzian space forms. 相似文献
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In this paper,the authors obtain the Backlund transformation on time-like surfaces with constant mean curvature in R2,1.Using this transformation,families of surfaces with constant mean curvature from known ones can be constructed. 相似文献
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Yan-Zhi Duan 《Journal of Mathematical Analysis and Applications》2009,351(1):186-613
In this paper, we investigate the asymptotic behavior of classical solutions of reducible quasilinear hyperbolic systems with characteristic boundaries. Under some suitable assumptions, we prove that the solution approaches a combination of Lipschitz continuous and piecewise C1 traveling wave solution. As an application, we apply the result to the equation for time-like extremal surfaces in the Minkowski space-time R1+(1+n). 相似文献