Questions tagged [isometry-groups]

Questions about the group of isometries of a metric space, in particular, a Riemannian manifold.

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Correspondence between Riemannian metrics and Euclidean embeddings

Given a sufficiently smooth manifold M, a Riemannian metric on M induces an isometric embedding into Euclidean space by Nash's theorem, (non-canonically, non-uniquely) an embedding of M into ...
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Let $G'\triangleleft G<\operatorname{Iso}(M)$ be a normal subgroup. A $G'$-stratum is the union of $G$-strata of lesser dimension

Let $G$ be a group of isometries acting effectively by isometries on a connected Riemannian manifold. And let $G'\triangleleft G$ be a normal subgroup. I am trying to prove that $\dim \operatorname{St}...
13
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2answers
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Possible isometry groups of open manifolds

Consider a non-compact manifold $M$. Does there always exist a Riemannian metric on $M$ such that the isometry group is non-compact?
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Can Riemann's explicit formula be generalized to semi-primes?

Following Isometry group of an integer I wonder if one can define a "mock zeta function" $\zeta_{V}$ (where $V:=(\mathbb{Z}/2\mathbb{Z})^{2}$ stands for "Vierergruppe", the German word for the Klein ...
3
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1answer
224 views

Closed Semi-Riemannian manifolds with non-compact isometry group

Does anyone know a good reference for general results about closed Semi-Riemannian manifolds which have a non-compact isometry group? Edit: My goal is to understand a bit better what the intuition ...