论文标题
欧几里得三个空间中两种差异性低的局部等距嵌入
The Local Isometric Embedding of Two-Metrics of Low Differentiability in Euclidean Three Space
论文作者
论文摘要
我们证明存在E3中C1中任何不同度量标准的等轴测嵌入。我们对给定的度量标准使用简化的符号，即E3中嵌入式表面的测量参数和级别参数。我们讨论的核心将是两个一阶非线性偏微分方程的初始价值问题的解决方案。我们还利用线性代数系统的经典理论。我们将证明局部等距嵌入。给出了一个示例，该示例是公制的高斯曲率等于一个，但嵌入的表面是非分析的。
We prove that the isometric embedding of any metric of differentiability class C1 in E3 exists. We use simplified notation for the given metric, namely geodesic parameters, and level parameters for the embedded surface in E3. Central to our discussion will be solutions of initial value problems for two first order non-linear partial differential equations. We also make use of the classical theory of linear algebraic systems. We will prove local isometric embedding. An example is given for which the Gaussian curvature of the metric is equal to one but the embedded surface is non-analytic.
