Symplectic frame bundle

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In symplectic geometry, the symplectic frame bundle[1] 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 .

See also[edit]


  1. ^ Habermann, Katharina; Habermann, Lutz (2006), Introduction to Symplectic Dirac Operators, Springer-Verlag, p. 23, ISBN 978-3-540-33420-0