论文标题
Riemann空间和PFAFF差异形式
Riemann spaces and Pfaff differential forms
论文作者
论文摘要
在这项工作中，我们使用PFAFF衍生物研究$ n $ dimensional Riemann弯曲空间中的差异几何形状。避免经典的部分衍生物以更复杂的方式构建PFAFF衍生物，并使评估变得更加容易。以这种方式，经典riemann几何形状的christofell符号$γ_{ikj} $以及公制张量$ g_ {ij} $的元素被用一个符号（$ q_ {ikj} $）代替。实际上，要描述空间，我们不需要使用度量张量$ g_ {ij} $的用法。我们也不使用爱因斯坦的符号，这也简化了很多事情。例如，我们不必使用上下索引，而在初学者的眼中，我们不必使用上下索引。另外，我们不使用张量的概念。形成张量场的所有数量的表面或曲线或空间称为空间的不变式或曲率。在此基础上开发了一些新想法。
In this work we study differential geometry in $N$ dimensional Riemann curved spaces using Pfaff derivatives. Avoiding the classical partial derivative the Pfaff derivatives are constructed in a more sophisticated way and make evaluations become easier. In this way Christofell symbols $Γ_{ikj}$ of classical Riemann geometry as also the elements of the metric tensor $g_{ij}$ are replaced with one symbol (the $q_{ikj}$). Actually to describe the space we need no usage of the metric tensor $g_{ij}$ at all. We also don't use Einstein's notation and this simplifies also things a lot. For example we don't have to use upper and lower indexes, which in eyes of a beginner, is quite messy. Also we don't use the concept of tensor. All quantities of the surface or curve or space which form a tensor field are called invariants or curvatures of the space. Several new ideas are developed in this basis.
