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Curvatures of spheres
in Hilbert geometry
Alexander Borisenko and Eugene Olin |
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Vol. 254 (2011), No. 2, 257–273
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Abstract |
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We prove that the normal curvatures of hyperspheres, the Rund curvature, and the Finsler curvature of circles in Hilbert geometry tend to 1 as the radii tend to infinity. |
Keywords
Hilbert geometry, Finsler geometry, spheres, norman
curvature, Rund curvature, Finsler curvature
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Mathematical Subject Classification 2010
Primary: 53B40, 53C60
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Milestones
Received: 10 May 2011
Accepted: 11 July 2011
Published: 27 February 2012
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Authors |
| Alexander Borisenko | |
| School of Mathematics and Mechanical
Engineering, Geometry Department Kharkov National University Svobody square, 4 Kharkov 61022 Ukraine |
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| Eugene Olin | |
| School of Mathematics and Mechanical
Engineering, Geometry Department Kharkov National University Svobody square, 4 Kharkov 61022 Ukraine |
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| http://geometry.univer.kharkov.ua/~olin/olin.html | |
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