- A -dimensional surface in a space (often a Euclidean space) of dimension +1
- 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.)