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$\DeclareMathOperator\SO{SO}$I'm not asking for a proof but for some hint that might be helpful to understand this "anomaly" in 4 dimensions. I'm aware of the parallelism with the $A_4$ ...

Say we have a Lie group $G$ acting transitively on smooth manifold $M$ and take a submanifold $S\subseteq M$. It seems to me that there should be some minimal subgroup $G'\subseteq G$ such that $S\...

Let $\Gamma$ be a discrete subgroup of the isometry group of $\mathbb R^n$ and $O=\mathbb R^n/\Gamma$ is the orbifold. If there exists a point $p \in O$ such that $$ \lim_{r \to \infty}\frac{\text{...

Let $X=G/H$ be a homogeneous manifold, where $G$ and $H$ are connected Lie groups and assume there is given a $G$-invariant Riemannian metric on $X$. Let $B(R)$ be the closed ball of radius $R>0$ ...

In this question, which we flag it as a community wiki question, we search for a big list of groups $G$ which can not be isomorphic to a structure mentioned in $i.$ for some $i \in \{1,2,\ldots,...

I'm trying to find an example of a Lie group $G$ which admits a bi-invariant Riemannian metric, and which has a closed subgroup $H$ such that the manifold $G/H$ does not admit a $G$-invariant ...