a subset of a manifold that is itself a manifold, but has smaller dimension

A submanifold is the image of a smooth embedding of a manifold.

In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S → M satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions.