submanifold
Noun
Meaning
submanifold (plural submanifolds)
(topology) A manifold which is a subset of another, so that the inclusion function is an embedding or, sometimes, an immersion.
Phrases with the word
Examples
A Lagrangian submanifold is called special if in addition to the above Lagrangian condition the restriction to is vanishing.
Lagrangian mapping Let L be a Lagrangian submanifold of a symplectic manifold (K,ω) given by an immersion i : L ↪ K (i is called a Lagrangian immersion).
More generally, if a given manifold is thought of as an embedded submanifold of Euclidean space one can picture a tangent space in this literal fashion.
The theorem is often used in situations where Ω is an embedded oriented submanifold of some bigger manifold on which the form ω is defined.