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The space of immersions parallel to a given immersion. (English) Zbl 0807.53042

In this paper we consider immersions \(f:M^ m \to \mathbb{R}^{m + k}\) with trivial normal holonomy group. If the endpoints of a parallel normal field on \(M\) are not focal points then they determine an immersion of \(M\) into \(\mathbb{R}^{m + k}\) with the same focal set as \(f\). We define a subspace of \(\mathbb{R}^ k\) whose points correspond to these parallel immersions and find some properties of this space such as an upper bound for the number of its connected components.
Reviewer: S.Carter (Leeds)

MSC:

53C40 Global submanifolds
53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
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