Intrinsic torsion classes of Riemannian structures

TL;DR

This paper investigates the classification of intrinsic torsion varieties related to G-structures on parallelizable Riemannian manifolds, with a detailed example involving orthogonal almost product structures on the Iwasawa manifold.

Contribution

It introduces the problem of classifying intrinsic torsion varieties and analyzes specific cases on the Iwasawa manifold, providing new insights into G-structures.

Findings

Classification of intrinsic torsion varieties for G-structures.

Explicit analysis of orthogonal almost product structures on the Iwasawa manifold.

New methods for studying intrinsic torsion in Riemannian geometry.

Abstract

This article introduces the problem of finding intrinsic torsion varieties associated to G-structures on a fixed parallelizable Riemannian manifold. As an illustration, the intrinsic torsion varieties of orthogonal almost product structures are analysed on the Iwasawa manifold.