Riemann geometry without indices

TL;DR

This paper introduces an index-free formalism for Riemann geometry using Clifford algebra-valued forms and a specific group action, simplifying complex computations in the field.

Contribution

It proposes a novel index-free approach leveraging Clifford algebra and group actions to streamline Riemann geometric calculations.

Findings

Simplifies Riemann geometry computations

Uses Clifford algebra-valued forms

Employs $rak{sl}_2 imes rak{sl}_2$ group action

Abstract

We suggest an index-free formalism allowing to simplify many computations in Riemann geometry. The main ingredients are forms with values in a Clifford algebra and an action of the group $\mathfrak{sl}_2\times \mathfrak{sl}_2$ on such forms.