Massive scalar field on (A)dS space from a massless conformal field in   $\mathbb{R}^6$
  We show how the equations for the scalar field (including the massive, massless, minimally and conformally coupled cases) on de Sitter and Anti-de Sitter spaces can be obtained from both the SO$(2,4)$-invariant equation $\square \phi = 0$ in $\mathbb{R}^6$ and two geometrical constraints defining the (A)dS space. Apart from the equation in $\mathbb{R}^6$, the results only follow from the geometry. 
E. Huguet, J. Queva and J. Renaud
gr-qc hep-th math-ph math.MP