A Connection on Manifolds with a Nilpotent Structure

TL;DR

This paper investigates connections compatible with nilpotent structures on manifolds, characterizes when curvature tensors are pure or hybrid, and examines the effects of conformal changes on these properties.

Contribution

It provides a classification of pure connections related to nilpotent structures and establishes conditions for curvature tensor purity on B-type manifolds.

Findings

Identifies all connections pure toward the nilpotent structure

Provides examples of manifolds with pure or hybrid curvature tensors

Shows conformal changes do not preserve curvature tensor purity on B-manifolds

Abstract

All the connections, pure toward the nilpotent structure, are found. Examples of manifolds, for which the curvature tensor is pure or hybrid, are given. For a manifold of B-type a necessary and sufficient condition for purity of the curvature tensor is proved. It is verified that the conformal change of the metric of a B-manifold does not retain its purity.