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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