Affine connections on the algebra of differential forms

TL;DR

This paper introduces semi-symmetric metric connections on the algebra of differential forms, computes their curvature and Ricci tensors, and explores related geometric structures and properties.

Contribution

It defines and analyzes various semi-symmetric metric connections and their curvature properties on the algebra of differential forms, extending geometric understanding.

Findings

Computed curvature and Ricci tensors for specific semi-symmetric metric connections.

Derived Gauss-Codazzi-Ricci equations for distributions on the algebra of differential forms.

Explored properties of canonical, Schouten, and Vrancreanu connections.

Abstract

In this paper, we define the semi-symmetric metric connection on the algebra of differential forms. We compute some special semi-symmetric metric connections and their curvature tensor and their Ricci tensor on the algebra of differential forms. We study the distribution on the algebra of differential forms and we get its Gauss-Codazzi-Ricci equations associated to the semi-symmetric metric connection. We also study the Lie derivative of the distribution on the algebra of differential forms. We define the canonical connection and the Schouten connection and the Vrancreanu connection on the algebra of differential forms and get some properties of these connections.