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ovoid$56945$ - translation to german
SPHERE-LIKE SURFACE IN PROJECTIVE SPACE OF DIMENSION D ≥ 3
Ovoid (Projective geometry)
ovoid
adj. eiförmig
egg shaped
SHAPE
Ovaloid; Ovoid; Egg shaped; Egg-shaped; Egg (geometry); Egg shape; Oval (geometry); Oval-shaped; Ovalular; Egg curve; Oviform
adj. oval; eierförmig; ei-ähnlich; in der Form eines Eis
Wikipedia
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:
- Any line intersects in at most 2 points,
- The tangents at a point cover a hyperplane (and nothing more), and
- 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.
An ovoid is a special type of a quadratic set.
Ovoids play an essential role in constructing examples of Möbius planes and higher dimensional Möbius geometries.
