Extensions of isometric embeddings of Pseudo-Euclidean metric polyhedra

TL;DR

This paper extends isometric embedding results for indefinite metric polyhedra into Minkowski space, providing a simple construction algorithm and extension properties for partial embeddings.

Contribution

It generalizes previous work by showing embeddings for all bounded vertex degree indefinite metric polyhedra and introduces an extension method for partial embeddings.

Findings

Embeddings into Minkowski space are possible for all bounded degree indefinite metric polyhedra.

A simple algorithm for constructing such embeddings is provided.

Partial embeddings in general position extend to full embeddings.

Abstract

We extend the results of B. Minemyer by showing that any indefinite metric polyhedron (either compact or not) with the vertex degree bounded from above admits an isometric simplicial embedding into a Minkowski space of the lowest possible dimension. We provide a simple algorithm of constructing such embeddings. We also show that every partial simplicial isometric embedding of such space in general position extends to a simplicial isometric embedding of the whole space.