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Qu'est-ce (qui) est ovoid$56944$ - définition

SPHERE-LIKE SURFACE IN PROJECTIVE SPACE OF DIMENSION D ≥ 3

Ovoid (Projective geometry)

Ovoid (projective geometry)

In projective geometry an ovoid is a sphere like pointset (surface) in a projective space of dimension . Simple examples in a real projective space are hyperspheres (quadrics).

https://en.wikipedia.org/wiki/Ovoid_(projective_geometry)

Odostomia laevigata

SPECIES OF MOLLUSC

Ovoid odostome

Odostomia laevigata, common name the ovoid odostome, is a species of sea snail, a marine gastropod mollusc in the family Pyramidellidae, the pyrams and their allies.Rosenberg, G.

https://en.wikipedia.org/wiki/Odostomia_laevigata

Ovoid (polar space)

CONCEPT IN MATHEMATICS

In mathematics, an ovoid O of a (finite) polar space of rank r is a set of points, such that every subspace of rank r-1 intersects O in exactly one point..

https://en.wikipedia.org/wiki/Ovoid_(polar_space)

Wikipédia

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 ${\mathcal {O}}$ are:

Any line intersects ${\mathcal {O}}$ in at most 2 points,
The tangents at a point cover a hyperplane (and nothing more), and
${\mathcal {O}}$ 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.

https://en.wikipedia.org/wiki/Ovoid (projective geometry)