Ovoid (projective geometry)
In projective geometry an ovoid is a sphere like pointset (surface) in a projective space of dimension d ≥ 3. Simple examples in a real projective space are hyperspheres (quadrics). The essential geometric properties of an ovoid are: 1.
* Any line intersects in at most 2 points, 2.
* The tangents at a point cover a hyperplane (and nothing more), and 3.
* contains no lines. Property 2) excludes degenerated cases (cones,...). Property 3) excludes ruled surfaces (hyperboloids of one sheet, ...). An ovoid is the spatial analog of an oval in a projective plane.
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Ovoid (projective geometry)
In projective geometry an ovoid is a sphere like pointset (surface) in a projective space of dimension d ≥ 3. Simple examples in a real projective space are hyperspheres (quadrics). The essential geometric properties of an ovoid are: 1.
* Any line intersects in at most 2 points, 2.
* The tangents at a point cover a hyperplane (and nothing more), and 3.
* contains no lines. Property 2) excludes degenerated cases (cones,...). Property 3) excludes ruled surfaces (hyperboloids of one sheet, ...). An ovoid is the spatial analog of an oval in a projective plane.
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Ein Ovoid ist in der projektiv ...... Räumen eine wesentliche Rolle.
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In projective geometry an ovoi ...... dimensional Möbius geometries.
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Ein Ovoid ist in der projektiv ...... Räumen eine wesentliche Rolle.
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In projective geometry an ovoi ...... an oval in a projective plane.
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Ovoid (Projektive Geometrie)
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Ovoid (projective geometry)
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