Robinson manifolds and the Chern-Robinson connection

TL;DR

This paper introduces the Chern-Robinson connection on almost Robinson manifolds, explores its curvature properties, derives Bianchi identities, and applies these findings to the geometry of Robinson manifolds.

Contribution

It defines a new connection on almost Robinson manifolds and analyzes its curvature, providing novel insights into their geometric structure.

Findings

Derived Bianchi identities for the Chern-Robinson connection

Analyzed curvature properties of the connection

Applied results to specific Robinson manifolds

Abstract

In this article, we define the Chern-Robinson connection on the complexify tangent bundle of an almost Robinson manifold and we study the curvature associated to. Various Bianchi identities are obtained together with an application to geometry of some Robinson manifolds.