CURVATURE BOUNDS OF EUCLIDEAN CONES OF SPHERES

Title & Authors
CURVATURE BOUNDS OF EUCLIDEAN CONES OF SPHERES
Chai, Y.D.; Kim, Yong-Il; Lee, Doo-Hann;

Abstract
In this paper, we obtain the optimal condition of the curvature bounds guaranteeing that Euclidean cones over Aleksandrov spaces of curvature bounded above preserve the curvature bounds, by considering the Euclidean cone CS$\small{_{r}}$ $\small{^{n}}$ over n-dimensional sphere S$\small{_{r}}$ $\small{^{n}}$ of radius r. More precisely, we show that for r<1, the Euclidean cone CS$\small{_{r}}$ $\small{^{n}}$ of S$\small{_{r}}$ $\small{^{n}}$ is a CBB(0) space, but not a CBA($\small{textsc{k}}$)-space for any real $\small{textsc{k}}$$\small{\in}$R.
Keywords
Euclidean cone;Aleksandrov spaces;interior metrics;
Language
English
Cited by
1.
The Deformation Spaces of Projective Structures on 3-Dimensional Coxeter Orbifolds, Geometriae Dedicata, 2006, 119, 1, 69
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