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