Invariants of contact sub-pseudo-Riemannian structures and Einstein-Weyl geometry

TL;DR

This paper studies the local geometry of contact sub-pseudo-Riemannian structures, constructs their fundamental invariants, and shows how they relate to Einstein-Weyl geometries under specific conditions.

Contribution

It introduces fundamental invariants for contact sub-pseudo-Riemannian structures and links these structures to Einstein-Weyl geometries in three dimensions.

Findings

Construction of fundamental invariants for the structures

Conditions under which structures induce Einstein-Weyl geometries

Establishment of a geometric correspondence in dimension 3

Abstract

We consider local geometry of sub-pseudo-Riemannian structures on contact manifolds. We construct fundamental invariants of the structures and show that the structures give rise to Einstein-Weyl geometries in dimension 3, provided that certain additional conditions are satisfied.