On the first Betti number of certain compact nearly cosymplectic manifolds (Q1926126)
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scientific article; zbMATH DE number 6118621
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the first Betti number of certain compact nearly cosymplectic manifolds |
scientific article; zbMATH DE number 6118621 |
Statements
On the first Betti number of certain compact nearly cosymplectic manifolds (English)
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27 December 2012
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Let \(M(\varphi,\xi,\eta,g)\) be a compact nearly cosymplectic manifold. Suppose \(H=\nabla\xi\), where \(\nabla\) is the Levi-Civita connection coming from the Riemannian metric \(g\). It is proved that if \(H\) is not identically zero and commutes with the Ricci operator \(Q\) on \(M\), then the first Betti number of \(M\) is zero or even. Certain consequences are discussed.
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nearly cosymplectic manifold
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Betti number
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Ricci curvature
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