New examples of compact cosymplectic solvmanifolds

J.C. Marrero, E. Padron

Address. Depto. Matematica Fundamental, Facultad de Matematicas, Universidad de la Laguna, Tenerife, Canary Islands, SPAIN


Abstract. 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 K\"ahler manifold with the circle $S^1.$

AMSclassification. Primary 53C15, 53C55; Secondary 22E25

Keywords. Cosymplectic manifolds, solvmanifolds, Kahler manifolds, suspensions, flat Riemannian manifolds