On the Structure of Submanifolds with Degenerate Gauss Mappings

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dc.creatorAkivis, Maks A.
dc.creatorGoldberg, Vladislav V.
dc.date2000-02-11
dc.date2000-06-08
dc.date.accessioned2026-07-07T04:33:50Z
dc.date.available2026-07-07T04:33:50Z
dc.descriptionAn n-dimensional submanifold X of a projective space P^N (C) is called tangentially degenerate if the rank of its Gauss mapping γ: X ---> G (n, N) satisfies 0 < rank γ< n. The authors systematically study the geometry of tangentially degenerate submanifolds of a projective space $P^N (\mathbf{C})$. By means of the focal images, three basic types of submanifolds are discovered: cones, tangentially degenerate hypersurfaces, and torsal submanifolds. Moreover, for tangentially degenerate submanifolds, a structural theorem is proven. By this theorem, tangentially degenerate submanifolds that do not belong to one of the basic types are foliated into submanifolds of basic types. In the proof the authors introduce irreducible, reducible, and completely reducible tangentially degenerate submanifolds. It is found that cones and tangentially degenerate hypersurfaces are irreducible, and torsal submanifolds are completely reducible while all other tangentially degenerate submanifolds not belonging to basic types are reducible.
dc.descriptionLaTeX, 22 pages; revised version, to appear in Geometrae Dedicata
dc.identifierhttps://arxiv.org/abs/math/0002093
dc.identifierhttp://arxiv.org/abs/math/0002093
dc.identifierGeom. Dedicata, 86 (2001) no. 1-3 205-226
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58674
dc.subjectDifferential Geometry
dc.subject53A20 (Primary), 14M99 (Secondary)
dc.titleOn the Structure of Submanifolds with Degenerate Gauss Mappings
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