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Homogeneous metric connections on 3-dimensional Lie groups
Let $G$ be a 3-dimensional unimodular Lie group equipped with a left-invariant metric $q$. Call $P_{SO}$ its oriented orthonormal frame bundle.
Considering the moduli space of connections $\mathscr{B}$...
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Is there an easy example of group action where the slice theorem produces a non-trivial principal bundle?
Let $\rho$ be a group action by a compact group $G$
\begin{equation}
\rho:G\times M \rightarrow M \\
\rho:(g,p) \rightarrow \rho_g(p)
\end{equation}
Denote the orbit of $p\in M$ by $\...
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