Riemann spaces and Pfaff differential forms

2020/05/05 by Nikos Bagis, Nikos D. Bagis, Bagis, Nikos D.
Engineering · Mathematics · #53A07 #53A45 #53A55 #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #Elasticity and Material Modeling #FOS: Mathematics #General Mathematics (math.GM) #math.GM #msc:53A07 #msc:53A45 #msc:53A55

paper · pdf · doi:10.48550/arxiv.2005.02763

Differential Geometry, 53 pages

openalex publication_date 2020/05/05 · arxiv created 2021/11/15 · arxiv updated 2021/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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