Abstract
Let M_k^2 be the complete, simply connected, Riemannian 2-manifold of constant curvature k ± 0. Let E be a closed, simply connected subspace of M_k^2 with the property that every two points in E are connected by a rectifi able path in E. We show that E is CAT(k) under the induced path metric.
Degree
MS
College and Department
Physical and Mathematical Sciences; Mathematics
Rights
http://lib.byu.edu/about/copyright/
BYU ScholarsArchive Citation
Ricks, Russell M., "Planar CAT(k) Subspaces" (2010). Theses and Dissertations. 2090.
https://scholarsarchive.byu.edu/etd/2090
Date Submitted
2010-03-10
Document Type
Thesis
Handle
http://hdl.lib.byu.edu/1877/etd3420
Keywords
CAT(k) spaces, Jordan Curve Theorem, nonpositive curvature, convexity
Language
English