In mathematics, an ovoid O of a (finite) polar space of rank r is a set of points, such that every subspace of rank
intersects O in exactly one point.
[1] An ovoid of
(a symplectic polar space of rank n) would contain
However it only has an ovoid if and only
In that case, when the polar space is embedded into
{\displaystyle PG(3,q)}
the classical way, it is also an ovoid in the projective geometry sense.
Ovoids of
points.
An ovoid of a hyperbolic quadric
An ovoid of a parabolic quadric
, it is easy to see to obtain an ovoid by cutting the parabolic quadric with a hyperplane, such that the intersection is an elliptic quadric.
The intersection is an ovoid.
is isomorphic (as polar space) with
, and thus due to the above, it has no ovoid for
An ovoid of an elliptic quadric