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 which...
- subspace to a submanifold is co-isotropic (the dual of an isotropic subspace), the submanifold is called co-isotropic. Lagrangian submanifolds of a symplectic...
- A Riemannian submanifold N of a Riemannian manifold M is a submanifold of M equipped with the Riemannian metric inherited from M. The image of an isometric...
- 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} the...
- immersed) submanifolds whose tangent spaces lie inside the contact field: these are called Legendrian submanifolds. Legendrian submanifolds are analogous...
- 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)...
- 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...
- intrinsically the property of being a hypersurface (or certain real submanifolds of higher codimension) in complex space by studying the properties of...
- However, 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 on...
- Currently the theory of minimal surfaces has diversified to minimal submanifolds in other ambient geometries, becoming relevant to mathematical physics...