In mathematics, a hypersurface is some kind of submanifold.

• For differential geometry usage, see glossary of differential geometry and topology.
• In algebraic geometry, a hypersurface in projective space of dimension n is an algebraic set that is purely of dimension n − 1. It is then defined by a single equation F = 0, a homogeneous polynomial in the homogeneous coordinates. (It may have singularities, so not in fact be a submanifold in the strict sense.)

See also: hyperplane, hypersphere, hyperspace.