- symplectic manifold
- мат. симплектическое многообразие
Большой англо-русский и русско-английский словарь. 2001.
symplectic manifold
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Symplectic manifold — In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2 form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology.… … Wikipedia
Almost symplectic manifold — In differential geometry, an almost symplectic structure on a differentiable manifold M is a two form ω on M which is everywhere non singular. If, in addition, ω is closed, then it is a symplectic form.An almost symplectic manifold is an Sp… … Wikipedia
Symplectic geometry — is a branch of differential topology/geometry which studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2 form. Symplectic geometry has its origins in the Hamiltonian formulation of classical… … Wikipedia
Symplectic cut — In mathematics, specifically in symplectic geometry, the symplectic cut is a geometric modification on symplectic manifolds. Its effect is to decompose a given manifold into two pieces. There is an inverse operation, the symplectic sum, that… … Wikipedia
Symplectic sum — In mathematics, specifically in symplectic geometry, the symplectic sum is a geometric modification on symplectic manifolds, which glues two given manifolds into a single new one. It is a symplectic version of connected summation along a… … Wikipedia
Symplectic filling — In mathematics, a filling of a manifold X is a cobordism W between X and the empty set. More to the point, the n dimensional topological manifold X is the boundary of an n+1 dimensional manifold W . Perhaps the most active area of current… … Wikipedia
Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… … Wikipedia
Symplectic vector space — In mathematics, a symplectic vector space is a vector space V equipped with a nondegenerate, skew symmetric, bilinear form omega; called the symplectic form. Explicitly, a symplectic form is a bilinear form omega; : V times; V rarr; R which is *… … Wikipedia
Symplectic group — For finite groups with all characteristc abelian subgroups cyclic, see group of symplectic type. Group theory … Wikipedia
Symplectic vector field — In physics and mathematics, a symplectic vector field is one whose flow preserves a symplectic form. That is, if (M,omega) is a symplectic manifold, then a vector field Xinmathfrak{X}(M) is symplectic if its flow preserves the symplectic… … Wikipedia
Symplectic space — A symplectic space is either a symplectic manifold or a symplectic vector space. The latter is a special case of the former … Wikipedia
