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Keywords:
cosymplectic manifolds; solvmanifolds; Kähler manifolds; suspensions; flat Riemannian manifolds
cosymplectic manifolds; solvmanifolds; Kähler manifolds; suspensions; flat Riemannian manifolds
Summary:
In this paper we present new examples of $(2n+1)$-dimensional compact cosymplectic manifolds which are not topologically equivalent to the canonical examples, i.e., to the pro\-duct of the $(2m+1)$-dimensional real torus and the $r$-dimensional complex projective space, with $m,r\geq 0$ and $m+r=n.$ These new examples are compact solvmanifolds and they are constructed as suspensions with fibre the $2n$-dimensional real torus. In the particular case $n=1,$ using the examples obtained, we conclude that a $3$-dimensional compact flat orientable Riemannian manifold with non-zero first Betti number admits a cosymplectic structure. Furthermore, if the first Betti number is equal to $1$ then such a manifold is not topologically equivalent to the global product of a compact Kähler manifold with the circle $S^1.$
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