Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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CURVATURE BOUNDS OF EUCLIDEAN CONES OF SPHERES

  • Chai, Y.D. (Department of Mathematics, Sungkyunkwan University) ;
  • Kim, Yong-Il (School of Media, Soongsil University) ;
  • Lee, Doo-Hann (Department of Mathematics, Sungkyunkwan University)
  • Published : 2003.05.01
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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$_{r}$ $^{n}$ over n-dimensional sphere S$_{r}$ $^{n}$ of radius r. More precisely, we show that for r<1, the Euclidean cone CS$_{r}$ $^{n}$ of S$_{r}$ $^{n}$ is a CBB(0) space, but not a CBA($textsc{k}$)-space for any real $textsc{k}$$\in$R.

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References

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