Differential Geometry中等距嵌入问题的流体动力学描述
A Fluid Dynamic Formulation of the Isometric Embedding Problem in Differential Geometry
摘要：
等距嵌入问题是微分几何中的一个基本问题。本文讨论了二维黎曼流形上的内蕴度量的一个长期存在的问题，该流形可以实现为三维欧几里得空间的等距浸入.气体动力学和微分几何之间的显着联系进行了讨论。它示出了如何流体动力学可以用来制定一个几何问题。首先回顾了气体动力学方程。在此基础上，利用气体动力学守恒律中的流体动力学变量，给出了微分几何中等距嵌入问题的求解公式。
英文摘要：
The isometric embedding problem is a fundamental problem in differential geometry. A longstanding problem is considered in this paper to characterize intrinsic metrics on a two-dimensional Riemannian manifold which can be realized as isometric immersions into the three-dimensional Euclidean space. A remarkable connection between gas dynamics and differential geometry is discussed. It is shown how the fluid dynamics can be used to formulate a geometry problem. The equations of gas dynamics are first reviewed. Then the formulation using the fluid dynamic variables in conservation laws of gas dynamics is presented for the isometric embedding problem in differential geometry.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
