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Angular distribution
of diameters for spheres and rays for planes
Nobuhiro Innami and Yuya Uneme |
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Vol. 277 (2015), No. 1, 169–185
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Abstract |
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Grove and Shiohama used the critical point theory of a distance function to prove the diameter sphere theorem. In light of the angular distribution of minimizing geodesics, we examine and develop the techniques in its proof to make some diameter sphere theorems and study complete noncompact manifolds, using a generalized Toponogov comparison theorem. |
Keywords
sphere, diameter, ray, plane
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Mathematical Subject Classification 2010
Primary: 53C20, 53C22
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Milestones
Received: 30 March 2014
Revised: 10 December 2014
Accepted: 15 December 2014
Published: 6 August 2015
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Authors |
| Nobuhiro Innami | |
| Department of Mathematics Faculty of Science Niigata University Niigata 950-2181 Japan |
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| Yuya Uneme | |
| Graduate School of Science and
Technology Niigata University Niigata 950-2181 Japan |
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