G-Structures defined on pseudo-Riemannian manifolds

TL;DR

This paper explores the application of higher-order G-structure theory to analyze various geometric structures on pseudo-Riemannian manifolds, investigating their relationships through operations like intersection and prolongation.

Contribution

It extends the theory of G-structures to pseudo-Riemannian manifolds, examining how different structures relate via operations such as reduction and extension.

Findings

Relationships between volume forms, conformal, linear, and projective structures established

Operations like intersection, inclusion, reduction, extension, and prolongation applied to G-structures

Framework for analyzing complex geometric structures on pseudo-Riemannian manifolds developed

Abstract

Concepts and techniques from the theory of G-structures of higher order are applied to the study of certain structures (volume forms, conformal structures, linear connections and projective structures) defined on a pseudo-Riemanniann manifold. Several relationships between the structures involved have been investigated. The operations allowed on G-structures, such as intersection, inclusion, reduction, extension and prolongation, were used for it.