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We prove that every symplectic manifold is a coadjoint orbit of the group of automorphisms of its integration bundle, acting linearly on its space of momenta, for any group of periods of the symplectic form. This result generalizes the Kirilov–Kostant–Souriau theorem when the symplectic manifold is homogeneous under the action of a Lie group and the symplectic form is integral.

We prove that every infinite-dimensional Banach space $X$ having a (not necessarily equivalent) real-analytic norm is real-analytic diffeomorphic to $X\,\backslash \,\left\{ 0 \right\}$. More generally, if $X$ is an infinite dimensional Banach space and $F$ is a closed subspace of $X$ such that there is a real-analytic seminorm on $X$ whose set of zeros is $F$, and $X/F$ is infinite-dimensional, then $X$ and $X\backslash F$ are real-analytic diffeomorphic. As an application we show the existence of real-analytic free actions of the circle and the $n$-torus on certain Banach spaces.

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Every symplectic manifold is a (linear) coadjoint orbit

NONLINEAR ANALYSIS IN GEODESIC METRIC SPACES

Real-Analytic Negligibility of Points and Subspaces in Banach Spaces, with Applications

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3 results

Every symplectic manifold is a (linear) coadjoint orbit

NONLINEAR ANALYSIS IN GEODESIC METRIC SPACES

Real-Analytic Negligibility of Points and Subspaces in Banach Spaces, with Applications