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Plane CurvesHeflin, Billy M. 01 1900 (has links)
The purpose of this thesis is to present a definition and some properties of a curved arc in a plane and to present a definition and some properties of the Jordan curve.
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Planar CAT(k) SubspacesRicks, Russell M. 10 March 2010 (has links) (PDF)
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.
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