Pseudo-Riemannian Lie groups of modified H-type

TL;DR

This paper introduces a new class of pseudo-Riemannian 2-step nilpotent Lie groups with nondegenerate centers, extending the concept of H-type groups and exploring their geometric properties.

Contribution

It generalizes H-type groups to pseudo-Riemannian settings and provides examples and geometric analysis of these new structures.

Findings

Defined a new class of pseudo-Riemannian Lie groups

Provided explicit examples of these groups

Investigated their geometric properties

Abstract

We define a class of Riemannian and pseudo-Riemannian 2-step nilpotent Lie groups with nondegenerate centers that generalize the H-type groups of Kaplan. Examples are given and geometric properties are investigated.