On the first Betti number of certain compact nearly cosymplectic manifolds
type: Item
instance of: scholarly article
title: On the first Betti number of certain compact nearly cosymplectic manifolds
zbMATH Open document ID: 1262.53040
author: Hiroshi Endo
published in: Journal of Geometry
publication date: 2012-12-27T00:00:00Z
review text: 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.
reviewed by: Zbigniew Olszak
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53D15
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 6118621
zbMATH Keywords: nearly cosymplectic manifold
zbMATH Keywords: Betti number
zbMATH Keywords: Ricci curvature
MaRDI profile type: Publication
full work available at URL: s00022-012-0126-2
OpenAlex ID: W2091346896
cites work: Contact manifolds in Riemannian geometry
cites work: Riemannian geometry of contact and symplectic manifolds
cites work: Q3432646
cites work: Q5424834
cites work: On harmonic tensors in compact Sasakian spaces
cites work: Q5615235
cites work: Q3222791
Wikidata QID: Q125635039
DOI: 10.1007/S00022-012-0126-2
description: scientific article; zbMATH DE number 6118621