Definition of Submanifold. Meaning of Submanifold. Synonyms of Submanifold

- In mathematics, a submanifold of a manifold M {\displaystyle M} is a subset S {\displaystyle S} which itself has the structure of a manifold, and for...
- immersed) submanifolds whose tangent spaces lie inside the contact field: these are called Legendrian submanifolds. Legendrian submanifolds are analogous...
- subspace to a submanifold is co-isotropic (the dual of an isotropic subspace), the submanifold is called co-isotropic. Lagrangian submanifolds of a symplectic...
- possibly disconnected). The submanifold Σ with the smallest number of boundary tori is called the characteristic submanifold of M; it is unique (up to isotopy)...
- when the curve γ {\displaystyle \gamma } is restricted to lie on a submanifold M {\displaystyle M} of M ¯ {\displaystyle {\bar {M}}} (e.g. for curves...
- true for any submanifold of Euclidean space of any dimension. Although John Nash proved that every Riemannian manifold arises as a submanifold of Euclidean...
- In mathematics, a (compact) taut submanifold N of a space form M is a compact submanifold with the property that for every q ∈ M {\displaystyle q\in M}...
- More generally, one can also join manifolds together along identical submanifolds; this generalization is often called the fiber sum. There is also a closely...
- thing as symplectic submanifolds. Another important generalisation of Poisson submanifolds is given by coisotropic submanifolds, introduced by Weinstein...
- A Riemannian submanifold N {\displaystyle N} of a Riemannian manifold M {\displaystyle M} is a submanifold N {\displaystyle N} of M {\displaystyle M}...