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gauss映射
相关语句
  gauss map
     The Gauss Map of Space-like Surfaces in R_2~4
     拟欧氏空间R_2~4中类空曲面的Gauss映射
短句来源
     When M_p~m is the hypersurface of E_q~n, H is just the classic Gauss map.
     当M_p~m是E_q~n的超曲面时,H就是经典的Gauss映射.
短句来源
     On the Gauss Map of Surfaces in R~4
     关于R~4中曲面的Gauss映射
短句来源
     The geometric of the generalized Gauss map in the case of surface in R~4
     R~4中曲面广义Gauss映射的几何
短句来源
     ON THE GAUSS MAP OF H - DEFORMABLE SURFACES
     关于H-变形曲面的Gauss映射
短句来源
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  gauss maps
     SOME RESULTS OF GAUSS MAPS
     关于Gauss映射的一些结果(英文)
短句来源
     The Pseudo-umbilical Surfaces in R~4 and Their Gauss Maps
     R~4中的伪脐曲面及Gauss映射(英文)
短句来源
     ON THE VOLUME OF GAUSS MAPS
     两种Gauss映射象体积的比较
短句来源
     In this paper we get another equal value condition[3] of the harmonic maps of the Riemann surface into G(k,n)by utilizing the standard method of moving frames and the internal geometry of G(k, n). And furthermore we use Gauss maps to extend the corresponding results of (3) to the situation in which the initial manifold is of an arbitrary kaehler manifold.
     本文利用活动标架的标准方法和G(k,n)的内在几何得到了从Riemann曲面到G(k,n)的调和映射的另一等价条件,再利用Gauss映射将〔3〕中相应结果推广到始流形为任意Kaehler流形的情形.
短句来源
  the gauss map
     The Gauss Map of Space-like Surfaces in R_2~4
     拟欧氏空间R_2~4中类空曲面的Gauss映射
短句来源
     On the Gauss Map of Surfaces in R~4
     关于R~4中曲面的Gauss映射
短句来源
     ON THE GAUSS MAP OF H - DEFORMABLE SURFACES
     关于H-变形曲面的Gauss映射
短句来源
     Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M , a sufficient condition is given for M as a flat torus in R 4 .
     本文研究了伪脐曲面M的一些性质 ,基于它并利用M的Gauss映射 ,给出了M作为R4中平坦环面的一个充分条件 .
短句来源
     On the Gauss map of weingarten surfaces
     W-曲面的Gauss映射
短句来源
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  “gauss映射”译为未确定词的双语例句
     GAUSS-LIKE MAPS
     类Gauss映射
短句来源
     Two Conclusions On Gauss Mapping Btween Two Surfaces
     关于曲面的GAUSS映射的两个结论
短句来源
     H is called the Gauss-like map.
     称H为类Gauss映射.
短句来源
     This paper, through discussing the relationships among three basic differential forms of a surface and its corresponding Gauss mapping image, generates two conclusions regarding the features of Gauss Mapping.
     讨论了曲面的Gauss映射象的三个基本微分形式与原曲面的三个基本形式之间的关系,得到了关于Gauss映射的性质的两个结论.
短句来源
     The most fundamental measure properties on Gauss mapping has been researched by means of Gauss mapping andby making use of the third fundamental form a surface.
     本文利用曲面的第三基本形式,来探求Gauss映射的一些最基本的度量性质。
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  gauss map
Bernshtein's theorem for a surface with quasiconformal Gauss map
      
We study a version of the Gauss map for a surface immersed in and prove an analog of the Ruh--Vilms theorem which states that this map is harmonic iff has a constant mean curvature.
      
The focusing directions of phonon images generated by the anisotropic propagation of ballistic phonons are interpreted as singularities of the Gauss map of the energy surface.
      
Some necessary and sufficient conditions that the twistor Gauss map is harmonic are given.
      
Singularities of de Sitter Gauss map of timelike hypersurface in Minkowski 4-space
      
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  gauss maps
Rigidity and mean curvature flow via harmonic Gauss maps
      
We investigate properties of harmonic Gauss maps and their applications to Lawson-Osserman's problem, to the rigidity of space-like submanifolds in a pseudo-Euclidean space and to the mean curvature flow.
      
In this paper we study surfaces in S4 and their twistor Gauss maps.
      
Stability of Frobenius pull-backs of tangent bundles and generic injectivity of Gauss maps in positive characteristic
      
On values of Gauss maps of complete minimal surfaces on annular ends
      
更多          
  the gauss map
We study a version of the Gauss map for a surface immersed in and prove an analog of the Ruh--Vilms theorem which states that this map is harmonic iff has a constant mean curvature.
      
The focusing directions of phonon images generated by the anisotropic propagation of ballistic phonons are interpreted as singularities of the Gauss map of the energy surface.
      
By interpreting the σ-nonlinear model as describing the Gauss map associated to a certain immersion, several classes of classical solutions for the 4-dimensional model are derived.
      
The stress-energy-momentum tensor of the Gauss map in the extended nonlinear σ-model
      
By interpreting the nonlinear σ-model as the Gauss map associated to a certain immersion, we derive an explicit connection between the energy-momentum tensor and the geometry of space-time.
      
更多          


The third fundamental form of a surface is the representation on the surface for the first fundamental form of a sphere. We want to research the intrinsic properties of Gauss mapping on the surface by means of the third fundamental form. It is the problem that we want to solve in this paper. The most fundamental measure properties on Gauss mapping has been researched by means of Gauss mapping andby making use of the third fundamental form a surface.

曲面的第三基本形式是球面的第一基本形式在曲面上的表示。考虑以第三基本形式为“尺子”,来研究曲面的Gauss象的内蕴性质,正是这篇文章所要解决的问题。本文利用曲面的第三基本形式,来探求Gauss映射的一些最基本的度量性质。

In this paper we get another equal value condition[3] of the harmonic maps of the Riemann surface into G(k,n)by utilizing the standard method of moving frames and the internal geometry of G(k, n). And furthermore we use Gauss maps to extend the corresponding results of (3) to the situation in which the initial manifold is of an arbitrary kaehler manifold.

本文利用活动标架的标准方法和G(k,n)的内在几何得到了从Riemann曲面到G(k,n)的调和映射的另一等价条件,再利用Gauss映射将〔3〕中相应结果推广到始流形为任意Kaehler流形的情形.

Let E_q~n be the n-dimensional Pseudo-Euclideun space with flat Pseudo-Riemannian metric of signature (q, n-q); M_p~m be the non-degenerate submanifold of E_q~n. If M_p~m is not the minimal submanifold of E_q~n, then we define a map H: M_p~m→Q=S_q~(n-1)(1) or H_(q-1)~(n-1)(1) (Pseudo-Riemannian sphere of Pseudo-hyperbolic space), such as H(x) =h(x)/||h(x) ||, X∈M_p~m, h(x) is the mean curvature vector at X of M_p~m in E_q~n. H is called the Gauss-like map. When M_p~m is the hypersurface of E_q~n, H is just the...

Let E_q~n be the n-dimensional Pseudo-Euclideun space with flat Pseudo-Riemannian metric of signature (q, n-q); M_p~m be the non-degenerate submanifold of E_q~n. If M_p~m is not the minimal submanifold of E_q~n, then we define a map H: M_p~m→Q=S_q~(n-1)(1) or H_(q-1)~(n-1)(1) (Pseudo-Riemannian sphere of Pseudo-hyperbolic space), such as H(x) =h(x)/||h(x) ||, X∈M_p~m, h(x) is the mean curvature vector at X of M_p~m in E_q~n. H is called the Gauss-like map. When M_p~m is the hypersurface of E_q~n, H is just the classic Gauss map. When we give a necessary and sufficient condition that the Gauss-like map is homothetic. Under certain conditions, we obtain the minimal property of the Gauss-like map and discuss the submanifold with total geoddsic Gauss-like map image.

设E_i~n是符号为(q,n-q)的伪欧氏空间,M_p~m是E_q~n的非退化子流形.如果M_p~m不是E_q~n的极小子流形,则定义一个映射H∶M_p~m→Q=S_q~(n-1)(1)或H_q~n=I(1)(伪黎曼球面与伪双曲空间),使得H(x)=h(x)/||h(x)||,x∈M_p~m,h(r)表示M_p~m在点x的平均曲率向量.称H为类Gauss映射.当M_p~m是E_q~n的超曲面时,H就是经典的Gauss映射.绘出了一个类Gauss映射是位似的充要条件.在一定条件下,得到了类Gauss映射的极小性并讨论了具有全测地类Gauss像的子流形.

 
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