In symplectic geometry, the symplectic frame bundle of a given symplectic manifold is the canonical principal -subbundle 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 . For , each fiber of the principal -bundle 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 .