  We consider in mean-field theory the continuous development below a
second-order phase transition of $n$-atic tangent plane order on a deformable
surface of genus zero with order parameter $\psi = \langle e^{i n \theta}
\rangle$. Tangent plane order expels Gaussian curvature. In addition, the total
vorticity of orientational order on a surface of genus zero is two. Thus, the
ordered phase of an $n$-atic on such a surface will have $2n$ vortices of
strength $1/n$, $2n$ zeros in its order parameter, and a nonspherical
equilibrium shape. Our calculations are based on a phenomenological model with
a gauge-like coupling between $\psi$ and curvature, and our analysis follows
closely the Abrikosov treatment of a type II superconductor just below
$H_{c2}$.
