Carter, Sheila; Şentürk, Zerrin The space of immersions parallel to a given immersion. (English) Zbl 0807.53042 J. Lond. Math. Soc., II. Ser. 50, No. 2, 404-416 (1994). 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) Cited in 5 ReviewsCited in 2 Documents MSC: 53C40 Global submanifolds 53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces Keywords:parallel normal field; focal set; parallel immersions PDFBibTeX XMLCite \textit{S. Carter} and \textit{Z. Şentürk}, J. Lond. Math. Soc., II. Ser. 50, No. 2, 404--416 (1994; Zbl 0807.53042) Full Text: DOI