Abstract

A review of geodesics and Busemann G-spaces is given. Aleksandrov curvature and the disjoint (0, n)-cells property are defined. We show how these properties are applied to and strengthened in Busemann G-spaces. We examine the relationship between manifolds and Busemann G-spaces and prove that all Riemannian manifolds are Busemann G-spaces, though not all metric manifolds are Busemann G-spaces. We show how Busemann G-spaces that also have bounded Aleksandrov curvature admit local closest-point projections to geodesic segments. Finally, we expound local properties of Busemann G-spaces and define a new property which we call the symmetric property. We show that Busemann G-spaces which have the disjoint (0,n)-cells property for every value of n cannot have the symmetric property.

Degree

MS

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2017-07-01

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd9427

Keywords

Busemann, geodesic, disjoint (0, n)-cells, Aleksandrov curvature

Included in

Mathematics Commons

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