A necessary flexibility condition of a nondegenerate suspension in Lobachevsky 3-space

TL;DR

This paper establishes a necessary condition for the flexibility of a nondegenerate suspension in Lobachevsky 3-space, linking edge lengths of the equator through a specific algebraic relation.

Contribution

It introduces a new necessary flexibility condition involving edge length combinations for suspensions in Lobachevsky 3-space.

Findings

A specific linear combination of edge lengths equals zero.

The condition applies to nondegenerate suspensions.

Provides a geometric criterion for flexibility in hyperbolic space.

Abstract

We show that some combination of the lengths of all edges of the equator of a flexible suspension in Lobachevsky 3-space is equal to zero (each length is taken either positive or negative in this combination).