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...
- |_{S}} is a symplectic form on S {\displaystyle S} . Isotropic submanifolds are submanifolds where the symplectic form restricts to zero, i.e. each tangent...
- immersed) submanifolds whose tangent spaces lie inside the contact field: these are called Legendrian submanifolds. Legendrian submanifolds are analogous...
- Hence isometric immersions and isometric embeddings are Riemannian submanifolds. For example, the n-sphere S n = { x ∈ R n + 1 : ‖ x ‖ = 1 } {\displaystyle...
- pertaining to the extended spectral subspace. The theory on spectral submanifolds extends to nonlinear non-autonomous systems of the form d x d t = A x...
- 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 Kähler form are calibrations, and the calibrated submanifolds are the complex submanifolds. This follows from the Wirtinger inequality. On a Calabi–Yau...
- symplectic submanifolds. More general classes of submanifolds play an important role in Poisson geometry, including Lie–Dirac submanifolds, Poisson–Dirac...
- 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...
- class of totally real submanifolds and of complex submanifolds; a slant submanifold of an almost Hermitian manifold is a submanifold for which there is a...