Journal of Geometry

, 109:25 | Cite as

The cone metric of a Busemann space

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Abstract

We introduce a metric \(d_c\) on the Busemann space (X, d) such that the horofunction compactification of the space \((X, d_c)\) is equivalent to the geodesic compactification of the initial space. The space \((X, d_c)\) is not geodesic in general. It is shown that \((X, d_c)\) is geodesic if and only if X is a real tree.

Keywords

Busemann space cone metric geodesic compactification 

Mathematics Subject Classification

Primary 53C23 Secondary 53C70 
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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Northern (Arctic) Federal UniversityArkhangelskRussia

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