On 3-dimensional \((\kappa,\mu,\nu)\)-contact metrics (Q2901331)
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scientific article; zbMATH DE number 6058394
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On 3-dimensional \((\kappa,\mu,\nu)\)-contact metrics |
scientific article; zbMATH DE number 6058394 |
Statements
19 July 2012
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contact metric 3-manifolds
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\((\kappa,\mu,\nu)\)-contact metric manifolds
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locally \(\varphi \)-symmetric
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cyclic parallel Ricci tensor
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\(\eta \)-parallel Ricci tensor
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Sasakian manifold
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On 3-dimensional \((\kappa,\mu,\nu)\)-contact metrics (English)
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Three-dimensional manifolds with a \((\kappa , \mu , \nu )\)-contact metric are studied under some conditions imposed on the Ricci tensor \(S\). More precisely, \(S\) is supposed cyclic-parallel or \(\eta \)-parallel or satisfying \(R(\xi , X)\cdot S=0\). A weaker version of locally symmetry called \textit{locally \(\varphi \)-symmetry} is searched on these manifolds.
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