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| On the Volume Formulas of Cones and Orthogonal Multi-cones in $S^n(1)$ and $H^n(-1)$ |
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Citation： |
Wu-Yi HSIANG.On the Volume Formulas of Cones and Orthogonal Multi-cones in $S^n(1)$ and $H^n(-1)$[J].Chinese Annals of Mathematics B,2006,27(1):1~30 |
| Page view： 1368
Net amount： 821 |
Authors： |
Wu-Yi HSIANG; |
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| Abstract： |
In the study of $n$-dimensional spherical or hyperbolic geometry,
$n\geq3$, the volume of various objects such as simplexes, convex
polytopes, etc. often becomes rather difficult to deal with. In
this paper, we use the method of infinitesimal symmetrization to
provide a systematic way of obtaining volume formulas of cones and
orthogonal multiple cones in $S^n(1)$ and $H^n(-1)$. |
Keywords： |
Hyperbolic geometry, Volume |
Classification： |
51M10, 51M20 |
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