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symplectic frame bundle

In symplectic geometry, the symplectic frame bundle of a given symplectic manifold(M,ω){\displaystyle (M,\omega )\,} is the canonical principal Sp(n,R){\displaystyle {\mathrm {Sp} }(n,{\mathbb {R} })}-subbundleπR:R→M{\displaystyle \pi _{\mathbf {R} }\colon {\mathbf {R} }\to M\,} of the tangent frame bundleFM{\displaystyle \mathrm {F} M\,} consisting of linear frames which are symplectic with respect to ω{\displaystyle \omega \,}.

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