十字帽形式幂级数的等距实现及其应用
Isometric realization of cross caps as formal power series and its applications
摘要：
欧氏$3$ -空间中的两个十字帽称为形式等距的，如果它们的第一基本型的泰勒展开式通过取适当的局部坐标系而重合.对于给定的$C^\infty$交叉帽$f$，我们给出了一种方法，找出所有形式上等距于$f$的交叉帽.作为应用，我们给出了一个可数族的交叉帽的固有不变量，它完全识别形式等距类。
英文摘要：
Two cross caps in Euclidean $3$-space are said to be formally isometric if their Taylor expansions of the first fundamental forms coincide by taking a suitable local coordinate system. For a given $C^\infty$ cross cap $f$, we give a method to find all cross caps which are formally isometric to $f$. As an application, we give a countable family of intrinsic invariants of cross caps which recognizes formal isometry classes completely.
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。
