A rigidity theorem for CR manifolds and a refinement of Obata and Lelong-Ferrand's result (Q2779216)
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scientific article; zbMATH DE number 1728054
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A rigidity theorem for CR manifolds and a refinement of Obata and Lelong-Ferrand's result |
scientific article; zbMATH DE number 1728054 |
Statements
15 April 2002
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CR manifold
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\(G\)-structure
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horospherical geometry
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quaternionic-conformally flat structure
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A rigidity theorem for CR manifolds and a refinement of Obata and Lelong-Ferrand's result (English)
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This is the main result: Let \(M\) be a compact strictly pseudoconvex CR manifold of dimension \(2n+1\). If the identity component \(\text{Aut}_{\text{CR}}(M)^0\) of the group of CR automorphisms is noncompact, then \(M\) is CR equivalent to the standard sphere \(\mathbb S^{2n+1}\). NEWLINENEWLINENEWLINEThe above result is the complex analogue of theorems by \textit{M. Obata} [J. Differ. Geom. 6, 247-258 (1971; Zbl 0236.53042)] and \textit{J. Lelong-Ferrand} [Mem. Cl. Sci., Collect. Octavo, Acad. R. Belg. 39, No. 5, 3-44 (1971; Zbl 0215.50902)]. The quaternionic analogue is also discussed.NEWLINENEWLINEFor the entire collection see [Zbl 0981.00018].
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