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- W976747424 abstract "In Section 3.1, we define the Monge-Ampere foliation associated with a variety with a degenerate Gauss map of dimension n, derive the basic equations of varieties with degenerate Gauss maps, and prove a characteristic property of such varieties (the Monge—Ampere foliation has flat leaves) of any of their plane generators. At the end of Section 3.1, for varieties with degenerate Gauss maps we prove the generalized Griffiths-Harris Theorem, which becomes the well-known Griffiths-Harris Theorem for tangentially nondegenerate varieties (see the paper [GH 79] by Griffiths and Harris). In Section 3.2, we consider focal images of such varieties (the focus hypersurfaces and the focus hypercones). In Section 3.3, we study varieties with degenerate Gauss maps without singularities, in Section 3.4, we introduce and investigate an important class of varieties with degenerate Gauss maps without singularities, the so-called Sacksteder-Bourgain hypersurface, in the affine space A4, and in Section 3.5, we consider complete parabolic varieties in Riemannian spaces of constant curvature." @default.
- W976747424 created "2016-06-24" @default.
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- W976747424 date "2004-01-01" @default.
- W976747424 modified "2023-09-27" @default.
- W976747424 title "Basic Equations of Varieties with Degenerate Gauss Maps" @default.
- W976747424 doi "https://doi.org/10.1007/0-387-21511-5_3" @default.
- W976747424 hasPublicationYear "2004" @default.
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