The Tilt Formula for Generalized Simplices in Hyperbolic Space |
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Authors: | Ushijima |
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Institution: | (1) Interactive Research Center of Science, Graduate School of Science and Engineering, Tokyo Institute of Technology, Tokyo 152—8551, Japan ushijima@math.titech.ac.jp, JP |
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Abstract: |
Abstract. For a simplex in Lorentzian space whose vertices are in the positive light cone, Weeks defined the ``tilt' relative to each
face. It gave us an efficient tool for deciding whether or not the dihedral angle between two simplices holding a face in
common is convex. He also provided an efficient formula, called the ``tilt formula,' to obtain tilts from the intrinsic hyperbolic
structure of the simplex when its dimension is two or three. Sakuma and Weeks generalized it to general dimensions. In this
paper we generalize the concept of the tilt and the tilt formula to the case where not all vertices are in the positive light
cone. A key to our generalization is to give a correspondence between points and hyperplanes (or half-spaces) in Lorentzian
space. |
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Keywords: | |
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