New Method for Building Geodesic Lines in Riemann Geometry

TL;DR

This paper introduces a novel approach for constructing geodesic lines in Riemann Geometry using differential forms, enhancing flexibility and scope of application in solving related differential equations.

Contribution

It presents a new perspective and method for deriving geodesic equations in Riemann Geometry utilizing differential forms without the need for completeness.

Findings

Extended the applicability of geodesic equations

Improved flexibility in equation transformation

Potential for broader application in differential geometry

Abstract

New perspective form of equations for geodesic lines in Riemann Geometry was found. This method is based on the use of differential forms in differential equations as arguments of differentiation. At that, these forms do not have a requirement of completeness, and that extends capabilities of equation transformation, makes their writing very flexible and extend their scope of application.