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.
Let be a metric space. A map is a geodesic bicombing if for all points the map is a unit speed metric geodesic from to , that is, , and for all real numbers . [3]
A geodesic bicombing is:
Examples of metric spaces with a conical geodesic bicombing include:
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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.
Let be a metric space. A map is a geodesic bicombing if for all points the map is a unit speed metric geodesic from to , that is, , and for all real numbers . [3]
A geodesic bicombing is:
Examples of metric spaces with a conical geodesic bicombing include:
{{
cite book}}
: CS1 maint: numeric names: authors list (
link)