Submanifold

In the differential geometry or differential topology a submanifold is a subset of a manifold that is compatible with the maps of the manifold.

Embedded submanifold

A subset of a - dimensional manifold is then exactly one -dimensional embedded submanifold, if for each point there exists a map such that the equation

Is satisfied. The sign denotes the tuple here. Each embedded submanifold is with the currently specified map and the induced subspace topology again a manifold.

Standard examples of submanifolds are the open sets of ( gleichdimensional ) or the equator of a sphere ( low-dimensional ). In general, the preimage of a regular value of a function is a submanifold of, see Theorem regular value.