Differential geometry MOC

Real embedded manifold

In these notes, a real embedded manifold typically refers to a submanifold of real coördinate space. #m/def/geo/diff The Whitney embedding theorem provides a sense in which every real differentiable manifold may be regarded as a real submanifold.

A subset is an -dimensional real submanifold iff has charts that are diffeomorphisms as subsets of real coördinate space, i.e. for every there exists a neighbourhood of in and an open set such that there exists a map with a right-inverse .

Properties

• Total derivative
• Tangent space

#state/tidy | #lang/en | #SemBr