The Darboux mapping of canal hypersurfaces

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The geometry of canal hypersurfaces of an n-dimensional conformal space C^n is studied. Such hypersurfaces are envelopes of r-parameter families of hyperspheres, 1 \leq r \leq n-2. In the present paper the conditions that characterize canal hypersurfaces, and which were known earlier, are made more precise. The main attention is given to the study of the Darboux maps of canal hypersurfaces in the de Sitter space M_1^{n+1} and the projective space P^{n+1}. To canal hypersurfaces there correspond r-dimensional spacelike tangentially nondegenerate submanifolds in M_1^{n+1} and tangentially degenerate hypersurfaces of rank r in P^{n+1}. In this connection the problem of existence of singular points on canal hypersurfaces is considered.
LaTeX, 19 pages; to be published in Beitraege Algebra Geom

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Differential Geometry, 53A30, 53A20, 53B25 (Primary) 53A35, 53A40 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/77117

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9807015
 http://arxiv.org/abs/math/9807015
 Beitraege Algebra Geom., 39 (1998) no. 2 396-411

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arXiv