Abstract A geometric triangulation of a Riemannian manifold is a triangulation where the interior of each simplex is totally geodesic. Bistellar moves are local changes to the triangulation which are higher dimensional versions of the flip operation of triangulations in a plane. We show that geometric triangulations of a compact hyperbolic, spherical or Euclidean manifold are connected by geometric bistellar moves (possibly adding or removing vertices), after taking sufficiently many derived subdivisions. For dimensions 2 and 3, we show that geometric triangulations of such manifolds are directly related by geometric bistellar moves (without having to take derived subdivision).

中文翻译：

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几何双星移动与几何三角测量相关

摘要 黎曼流形的几何三角剖分是其中每个单纯形内部完全是测地线的三角剖分。双星移动是三角测量的局部变化，三角测量是平面中三角测量的翻转操作的高维版本。我们表明，在采用足够多的衍生细分后，紧凑双曲线、球面或欧几里得流形的几何三角剖分通过几何双星移动（可能添加或删除顶点）连接。对于维度 2 和 3，我们表明此类流形的几何三角剖分与几何双星移动直接相关（无需进行衍生细分）。