Symplectic frame bundle
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.Books
