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arXiv · 1601.06265

Isometric realization of cross caps as formal power series and its applications

Atsufumi Honda·Kosuke Naokawa·Masaaki Umehara·Kotaro Yamada
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Abstract

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.

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Atsufumi Honda, Kosuke Naokawa, Masaaki Umehara, Kotaro Yamada. 2016-01-23. Isometric realization of cross caps as formal power series and its applications. https://arxiv.org/abs/1601.06265

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