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Let $M$ be a connected closed conformal oriented manifold.

Assume there exist conformal covering maps $\phi_k:M\to M$ of all degrees $k\geq 1$. Is $M\cong S^1$ then?

Let $M$ be a connected closed conformal oriented manifold.

Assume there exist conformal covering maps $\phi_k:M\to M$ of all degrees $k\geq 1$. Is $M\cong S^1$ then?

Can we at least rule out $\mathrm{dim}(M)=3$?

Let $M\neq S^1$ be a connected closed conformal oriented manifold. Can there exist conformal covering maps $\phi_k:M\to M$ of all degrees $k\geq 1$?

Let $M$ be a connected closed conformal oriented manifold.

Assume there exist conformal covering maps $\phi_k:M\to M$ of all degrees $k\geq 1$. Is $M\cong S^1$ then?