Geodesic bicombing

In metric geometry, a geodesic bicombing distinguishes a class of geodesics of a metric space.

The study of metric spaces with distinguished geodesics traces back to the work of the mathematician Herbert Busemann.

[1] The convention to call a collection of paths of a metric space bicombing is due to William Thurston.

[2] By imposing a weak global non-positive curvature condition on a geodesic bicombing several results from the theory of CAT(0) spaces and Banach space theory may be recovered in a more general setting.

be a metric space.

σ :

is a geodesic bicombing if for all points

is a unit speed metric geodesic from

for all real numbers

[3] A geodesic bicombing

is: Examples of metric spaces with a conical geodesic bicombing include: