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Spherical gradient manifolds

Christian Miebach; Henrik Stötzel — 2010

Annales de l’institut Fourier

We study the action of a real-reductive group $G = K exp (𝔭)$ on a real-analytic submanifold $X$ of a Kähler manifold. We suppose that the action of $G$ extends holomorphically to an action of the complexified group $G^{ℂ}$ on this Kähler manifold such that the action of a maximal compact subgroup is Hamiltonian. The moment map induces a gradient map $μ_{𝔭} : X \to 𝔭$ . We show that $μ_{𝔭}$ almost separates the $K$ –orbits if and only if a minimal parabolic subgroup of $G$ has an open orbit. This generalizes Brion’s characterization of spherical...

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