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

2016/01/23 by Honda, Atsufumi, Naokawa, Kosuke, Umehara, Masaaki +1 · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Primary 57R45 #Secondary 53A05

paper · doi:10.48550/arxiv.1601.06265

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^∞ 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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• Geometry on curves which go around a Whitney umbrella

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