Spaces with Non-Positive Curvature

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Yavartanoo, Fatemeh | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 42649 (02)
University: Sharif University of Technology
Department: Mathematical Science
Advisor(s): Fanai, Hamid Reza
Abstract:
There are different approaches to the ideal closure of geodesic metric space with non-positive curvature in the sense of Busemann. We established relations between them with Andreev theorem. In this theorem we introduced a continuous surjection which coincides with identity mapping of Idx onto X. Due to we studied metric spaces, geodesics and their angles and also CATk domains. Then with asymptotic rays we introduced metric boundary and we produced compact metric space. Then we proved Andreev theorem with some theorems and lemmas. The Andreev theorem is correct for Alexandrov space. Finally we construct the counterexample showing that Busemann ideal closure can differ from the geodesic closure
Keywords:
Geodesic Curvature ; Nonpositive Curvature ; Busemann Space ; Busemann Function ; Horo Function ; Metric Boundary ; CAT (0)-Space ; Geodesic Boundary

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