Homogeneity and local symmetry of complex (\(\kappa, \mu)\)-spaces (Q1758985)
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scientific article; zbMATH DE number 6108426
| Language | Label | Description | Also known as |
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| English | Homogeneity and local symmetry of complex (\(\kappa, \mu)\)-spaces |
scientific article; zbMATH DE number 6108426 |
Statements
Homogeneity and local symmetry of complex (\(\kappa, \mu)\)-spaces (English)
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19 November 2012
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The homogeneity and local symmetry of complex \((\kappa,\mu)\)-spaces is studied. The main results are the following two theorems. Theorem A. A complex \((\kappa,\mu)\)-space \((M,u,v,U,V,G,H,g)\) with \(\kappa<1\) has a homogeneous structure. Therefore, a complex \((\kappa,\mu)\)-space \(M\) with \(\kappa<1\) is locally homogeneous. Moreover, if the space \(M\) is complete, connected and simply connected, the complex \((\kappa,\mu)\)-space \((\kappa<1)\) \(M\) is homogeneous. Theorem B. A complex \((\kappa,\mu)\)-space has either \(\kappa=1\) or is \(GH\)-locally symmetric.
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complex contact metric manifold
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\((\kappa,\mu)\)-space
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locally homogeneous space
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locally symmetric space
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