# Large and Small Conformal Groups

It's well-known that on a Riemannian manifold $(M,g)$ with dimension larger than 2, the dimension of its conformal group $\text{conf}(M,g)$ is bounded above by ${n+2\choose 2}$. A Riemannian manifold whose conformal group has the maximum possible dimension is said to have a "large" conformal group. Some important examples include semisimple Lie groups that act by fractional linear transformations on manifolds, such as $SO(n+1,1)$, the conformal group of the standard $n$-sphere, and $SO(4,2)$, the conformal group of Minkowski space.

Now let's call any Lie group of transformations on $(M,g)$ "small" if that group is a discrete group.

There are plenty of examples of Riemannian manifolds with small isometry groups. In fact there's a neat paper (Asimov, 1976) which shows that if $G_{k+1}$ is a finite group with $k+1$ elements, then there exists a Riemannian metric on the $(k-1)$-sphere such that its isometry group is isomorphic to $G_{k+1}$.

Question: Are there examples of Riemannian manifolds with small conformal groups?