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- W3216839932 abstract "We study isometric actions of compact Lie groups on complete orientable positively curved $n$-manifolds whose orbit spaces have non-empty boundary in the sense of Alexandrov geometry. In particular, we classify quotients of the unit sphere with non-empty boundary. We deduce from this the list of representations of simple Lie groups that admit non-trivial reductions. As a tool of special interest, we introduce a new geometric invariant of a compact symmetric space, namely, the minimal number of points in a ``spanning set'' of the space." @default.
- W3216839932 created "2021-12-06" @default.
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- W3216839932 date "2021-12-01" @default.
- W3216839932 modified "2023-09-27" @default.
- W3216839932 title "Actions on positively curved manifolds and boundary in the orbit space." @default.
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