Homogeneous Lagrangian submanifolds

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Abstract

We characterize isometric actions on compact Kaehler manifolds admitting a Lagrangian orbit, describing under which condition the Lagrangian orbit is unique. We furthermore give the complete classification of simple groups acting on the complex projective space with a Lagrangian orbit, and we give the explicit list of these orbits.

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Calibrated geometries

REESE HARVEY, H. Lawson (1982)

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A classification of irreducible prehomogeneous vector spaces and their relative invariants

M Sato, E T Kimura (1977)

Let G be a connected linear algebraic group, and p a rational representation of G on a finite-dimensional vector space V, all defined over the complex number field C.