For differential geometry usage, see glossary of differential geometry and topology.

In geometry, a hypersurface is a generalization of the concept of hyperplane. Suppose an enveloping manifold M has n dimensions; then any submanifold of M of n − 1 dimensions is a hypersurface. Equivalently, the codimension of a hypersurface is one. For example, the n-sphere in R is called a hypersphere. Hypersurfaces occur frequently in multivariable calculus as level sets.