Stretched non-positive Weyl connections on solvable Lie groups

TL;DR

This paper classifies solvable Lie groups with invariant stretched non-positive Weyl connections, providing a complete characterization in four dimensions and identifying which admit such geometric structures.

Contribution

It offers a comprehensive classification of solvable Lie groups with invariant SNP connections, including a full dimension 4 classification and examples of admitting and non-admitting groups.

Findings

Complete classification of 4D solvable Lie groups with SNP connections

Identification of groups admitting or not admitting SNP connections

New insights into geometric structures on solvable Lie groups

Abstract

We determine the structure of solvable Lie groups endowed with invariant stretched non-positive Weyl connections and find classes of solvable Lie groups admitting and not admitting such connections. In dimension 4 we fully classify solvable Lie groups and compact solvmanifolds which admit invariant SNP connections.