锥化、对称性和球面框架
Coning, symmetry and spherical frameworks
摘要：
在本文中，我们结合单独的工作（a）转移的无穷小刚性结果从一个欧几里得空间下一个更高的维度锥，（b）进一步转移这些结果通过相关的刚性矩阵到球面空间，和（c）的预测有限运动的对称无穷小运动在正则点的轨道刚度矩阵。这些技术中的每一种都经过重新设计和简化，以应用于若干度量，包括闵可夫斯基度量$\M^{d}$和双曲度量$\H^{d}$。这导致了一组新的结果转移无穷小和有限的运动与相应的对称框架之间的$\E^{d}$，锥在$E^{d+1}$，$\SS^{d}$，$\M^{d}$，和$\H^{d}$。我们还考虑了与其他Cayley-Klein几何覆盖在共享的基础射影几何的进一步扩展。
英文摘要：
In this paper, we combine separate works on (a) the transfer of infinitesimal rigidity results from an Euclidean space to the next higher dimension by coning, (b) the further transfer of these results to spherical space via associated rigidity matrices, and (c) the prediction of finite motions from symmetric infinitesimal motions at regular points of the symmetry-derived orbit rigidity matrix. Each of these techniques is reworked and simplified to apply across several metrics, including the Minkowskian metric $\M^{d}$ and the hyperbolic metric $\H^{d}$. This leads to a set of new results transferring infinitesimal and finite motions associated with corresponding symmetric frameworks among $\E^{d}$, cones in $E^{d+1}$, $\SS^{d}$, $\M^{d}$, and $\H^{d}$. We also consider the further extensions associated with the other Cayley-Klein geometries overlaid on the shared underlying projective geometry.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
