A Sequence of Generalizations of Cartan's Conservation of Torsion Theorem

TL;DR

This paper presents a series of generalizations of Cartan's conservation of torsion theorem applicable to n-dimensional manifolds with a general linear connection, expanding the theoretical framework of differential geometry.

Contribution

It introduces a sequence of new theorems that extend Cartan's original conservation law for torsion to higher dimensions and more general connections.

Findings

Generalized conservation laws for torsion in n-dimensional manifolds.

Extension of Cartan's theorem to broader classes of linear connections.

Theoretical framework for future research in differential geometry.

Abstract

A sequence of generalizations of Cartan's conservation of torsion theorem is given for n-dimensional differentiable manifolds having a general linear connection.