A topological product decomposition of Busemann space

Abstract

We show that a Busemann space 𝑋 covered by parallel bi-infinite geodesics is homeomorphic to a product of another Busemann space 𝑌 and the real line. We also show that a semi-simple isometry on 𝑋 preserving the foliation by parallel geodesics canonically induces a semi-simple isometry on 𝑌.