|
Description: |
In this talk, we deal with 3-cosymplectic manifolds which are the closest odd-dimensional analogue of hyper-Kähler structures, just as cosymplectic manifolds are the closest odd-dimensional analogue of Kähler structures. After a brief introduction to the geometric properties of cosymplectic and 3-cosymplectic manifolds, we will focus on their topological properties.
We show that there is an action of the Lie algebra so(4, 1) on the basic cohomology spaces of a compact 3-cosymplectic manifold with respect to the Reeb foliation. This implies some topological obstructions to the existence of such structures which are expressed by bounds on the Betti numbers. Finally, we present a non-trivial example of a compact 3-cosymplectic manifold that is not the global product of a hyper-Kähler manifold and a flat 3-torus.
|
