Two types of Lie Groups as 4-dimensional Riemannian manifolds with circulant structure

TL;DR

This paper explores 4-dimensional Riemannian manifolds with circulant structures derived from specific Lie groups, analyzing their geometric properties and classifications based on algebraic types.

Contribution

It introduces a new class of manifolds with circulant structures on Lie groups and examines their geometric characteristics, expanding understanding of such structures.

Findings

Manifolds constructed on two types of Lie groups.

Circulant structure acts as an isometry.

Geometric characteristics of these manifolds are derived.

Abstract

A 4-dimensional Riemannian manifold equipped with an endomorphism of the tangent bundle, whose fourth power is the identity, is considered. The matrix of this structure in some basis is circulant and the structure acts as an isometry with respect to the metric. Such manifolds are constructed on 4-dimensional real Lie groups with Lie algebras of two remarkable types. Some of their geometric characteristics are obtained.