  We consider the group manifold approach to higher spin theory. The deformed
local higher spin transformation is realized as the diffeomorphism
transformation in the group manifold $\textbf{M}$. With the suitable rheonomy
condition and the torsion constraint imposed, the unfolded equation can be
obtained from the Bianchi identity, by solving which, fields in $\textbf{M}$
are determined by the multiplet at one point, or equivalently, by
$(W^{[a(s-1),b(0)]}_{\mu},H)$ in $AdS_{4}\subset \textbf{M}$. Although the
space is extended to $\textbf{M}$ to get the geometrical formulation, the
dynamical degrees of freedom are still in $AdS_{4}$. The $4d$ equations of
motion for $(W^{[a(s-1),b(0)]}_{\mu},H)$ are obtained by plugging the rheonomy
condition into the Bianchi identity. The proper rheonomy condition allowing for
the maximum on-shell degrees of freedom is given by Vasiliev equation. We also
discuss the theory with the global higher spin symmetry, which is in parallel
with the WZ model in supersymmetry.
