Loading AI tools
From Wikipedia, the free encyclopedia
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 .
Seamless Wikipedia browsing. On steroids.
Every time you click a link to Wikipedia, Wiktionary or Wikiquote in your browser's search results, it will show the modern Wikiwand interface.
Wikiwand extension is a five stars, simple, with minimum permission required to keep your browsing private, safe and transparent.