Isometric Deformation of Surfaces in the Hyperbolic 3-Manifold Preserving the Mean Curvature
Isometric Deformation of Surfaces in the Hyperbolic 3-Manifold Preserving the Mean Curvature
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双曲 3 流形中表面的等距变形保持平均曲率
DOI：
10.3836/tjm/1270043625
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发表时间：
1995
影响因子：
0.6
通讯作者：
H. Takeuchi
中科院分区：
文献类型：
--
作者：
H. Takeuchi
其中$H_{t}$表示$X_{t}$的平均曲率。一个H-变形$\{X_{t}\}$是平凡的，如果对于每个参数$t$，存在$N^{3}（c）$的等距$L$使得$X_{t}=L\circ X_{0}$。等距浸入$X$称为局部H-可变形的，如果$M$的每个点都有一个邻域限制$X$是H-可变形的。三维欧氏空间中的H-可变形曲面已有一些研究成果。O. Bonnet [1]证明了欧氏空间中的常平均曲率曲面可以保持平均曲率局部等距变形。E. Cartan [4]研究了具有非常数平均曲率的曲面的这种变形，并证明了它们是W-曲面。Chen和Peng [5]和K. Kenmotsu [8]在一些细节上刻画了曲面的黎曼度量和平均曲率函数。Colares和Kenmotsu [7]和Kespersos [14]证明了如果欧氏空间中的一个常高斯曲率曲面是局部H-可变形的，则高斯曲率必须为零，并且这种变形从对数螺线上的圆柱开始。Kokubu [9]研究了欧氏n-空间$（n\geq 3）$中超曲面的这种变形。
where $H_{t}$ denotes the mean curvature of $X_{t}$ . An H-deformation $\{X_{t}\}$ is trivial if for each parameter $t$ , there exists an isometry $L$ of $N^{3}(c)$ such that $X_{t}=L\circ X_{0}$ . An isometric immersion $X$ is called locally H-deformable if each point of $M$ has a neighborhood restricted to which $X$ is H-deformable. There are some papers on the H-deformable surfaces in Euclidean 3-space. O. Bonnet [1] proved that a surface of constant mean curvature in Euclidean space can be locally isometrically deformed preserving the mean curvature. \’E. Cartan [4] has studied such deformations for surfaces of nonconstant mean curvature and showed that they are W-surfaces. Chen and Peng [5] and K. Kenmotsu [8] characterized in some detail the Riemannian metrics and the mean curvature functions of the surfaces. Colares and Kenmotsu [7] and Roussos [14] proved that if a surface of constant Gaussian curvature in Euclidean 3-space is locally H-deformable, then the Gaussian curvature must be zero and such a deformation starts from a cylinder over a logarithmic spiral. Kokubu [9] studied such a deformation of hypersurfaces in Euclidean n-space $(n\geq 3)$ .
影响因子：
2.5
作者：
H. Lawson, Jr.;R. Tribuzy
通讯作者：
H. Lawson, Jr.;R. Tribuzy