Curvature without connection

TL;DR

This paper demonstrates that the theory of geometric structures can be developed without relying on connections, offering an alternative perspective to traditional approaches in differential geometry.

Contribution

It introduces a connection-independent framework for geometric structures, expanding the foundational understanding of geometric theories.

Findings

Geometric structures can be formulated without connections

Provides an alternative approach to classical differential geometry

Potentially simplifies the study of geometric structures

Abstract

We show that the theory of geometric structures proposed in the recent book "An Alternative Approach to Lie Groups and Geometric Structures" can be developed independently of connections.