Connections with skew-symmetric Ricci tensor on surfaces

TL;DR

This paper extends known results on torsionfree connections with skew-symmetric Ricci tensor on surfaces to include connections with torsion and simplifies Wong's canonical coordinate form for these connections.

Contribution

It generalizes existing theories to torsion connections and provides a simplified canonical coordinate form for such connections.

Findings

Extended results to connections with torsion.

Simplified Wong's canonical coordinate form.

Enhanced understanding of skew-symmetric Ricci tensor connections.

Abstract

Some known results on torsionfree connections with skew-symmetric Ricci tensor on surfaces are extended to connections with torsion, and Wong's canonical coordinate form of such connections is simplified.