The Ptolemaean Inequality in H--type groups

TL;DR

This paper extends classical geometric inequalities to the setting of H-type groups of Iwasawa-type, establishing the Ptolemaean Inequality and Ptolemaeus' Theorem within this non-Euclidean context.

Contribution

It introduces the first proof of the Ptolemaean Inequality and Ptolemaeus' Theorem specifically for H-type groups of Iwasawa-type, broadening geometric analysis in these groups.

Findings

Proved the Ptolemaean Inequality in H-type groups

Established Ptolemaeus' Theorem in the same setting

Extended classical Euclidean inequalities to non-Euclidean groups

Abstract

We prove the Ptolemaean Inequality and the Theorem of Ptolemaeus in the setting of $H$--type groups of Iwasawa--type.