Do co-adjoint orbits of Lie groups support a Kähler structure? We study this question from point view derived coherent states. examine three examples groups: the Weyl–Heisenberg group, SU(2) and SU(1, 1). In cases, where admit structure, we show that states give us embedding orbit into projective Hilbert space. contrast, squeezed (which like states, also saturate uncertainty bound) only symplec...