On the first Betti number of certain compact nearly cosymplectic manifolds
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.
scientific article; zbMATH DE number 6118621