Abstract
In the study of n-dimensional spherical or hyperbolic geometry, n≥ 3, 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).
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(Dedicated to the memory of Shiing-Shen Chern)
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Hsiang, WY. On the Volume Formulas of Cones and Orthogonal Multi-cones in S n(1) and H n(—1). Chin. Ann. Math. Ser. B 27, 1–30 (2006). https://doi.org/10.1007/s11401-005-0247-0
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DOI: https://doi.org/10.1007/s11401-005-0247-0