Definition of Submanifolds. Meaning of Submanifolds. Synonyms of Submanifolds

- called a closed embedded submanifold of M {\displaystyle M} . Closed embedded submanifolds form the nicest class of submanifolds. Smooth manifolds are sometimes...
- immersed) submanifolds whose tangent spaces lie inside the contact field: these are called Legendrian submanifolds. Legendrian submanifolds are analogous...
- |_{S}} is a symplectic form on S {\displaystyle S} . Isotropic submanifolds are submanifolds where the symplectic form restricts to zero, i.e. each tangent...
- thing as symplectic submanifolds. Another important generalisation of Poisson submanifolds is given by coisotropic submanifolds, introduced by Weinstein...
- 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)...
- intrinsically the property of being a hypersurface (or certain real submanifolds of higher codimension) in complex space by studying the properties of...
- Hence isometric immersions and isometric embeddings are Riemannian submanifolds. For example, the n-sphere S n = { x ∈ R n + 1 : ‖ x ‖ = 1 } {\displaystyle...
- topological submanifolds. In the category of topological manifolds, locally flat submanifolds play a role similar to that of embedded submanifolds in the category...
- topology, an area of mathematics, a neat submanifold of a manifold with boundary is a kind of "well-behaved" submanifold. To define this more precisely, first...
- submanifolds provide a greater generality, used to tackle several PDEs imposed on submanifolds of a given manifold, such as Lagrangian submanifolds and...