Symplectic frame bundle

In symplectic geometry, the symplectic frame bundle[1] of a given symplectic manifold

is the canonical principal

π

of the tangent frame bundle

consisting of linear frames which are symplectic with respect to

In other words, an element of the symplectic frame bundle is a linear frame

at point

i.e. an ordered basis

of tangent vectors at

of the tangent vector space

, satisfying for

of the principal

is the set of all symplectic bases of

The symplectic frame bundle

, a subbundle of the tangent frame bundle

, is an example of reductive G-structure on the manifold

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