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July 2020 Planar subspaces are intrinsically CAT(0)
Russell Ricks
Tsukuba J. Math. 44(1): 139-153 (July 2020). DOI: 10.21099/tkbjm/20204401139

Abstract

Let $M^2_{\kappa}$ be the complete, simply connected, Riemannian 2-manifold of constant curvature $\kappa \leq 0$. Let $E$ be a closed, simply connected subspace of $M^2_{\kappa}$ with the property that every pair of points in $E$ is connected by a rectifiable path in $E$. We show that under the induced path metric, $E$ is a complete CAT($\kappa$) space. We also show that the natural notions of angle coming from the intrinsic and extrinsic metrics coincide for all simple geodesic triangles.

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Russell Ricks. "Planar subspaces are intrinsically CAT(0)." Tsukuba J. Math. 44 (1) 139 - 153, July 2020. https://doi.org/10.21099/tkbjm/20204401139

Information

Published: July 2020
First available in Project Euclid: 22 December 2020

MathSciNet: MR4194196
Digital Object Identifier: 10.21099/tkbjm/20204401139

Subjects:
Primary: 53C22, 53C45

Keywords: CAT(0), curvature, planar

Rights: Copyright © 2020 University of Tsukuba, Institute of Mathematics

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Vol.44 • No. 1 • July 2020
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