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Description: |
In the talk I will present the main results of our systematic study of
3-quasi-Sasakian manifolds, conducted in collaboration with B. Cappelletti
Montano and G. Dileo. In particular we prove that the three
Reeb vector fields generate an involutive distribution determining a
canonical totally geodesic and Riemannian foliation. Locally, the
leaves of this foliation turn out to be Lie groups: either the
orthogonal group or an abelian one. We show that 3-quasi-Sasakian
manifolds have a well-defined rank, since the ranks of the three
Sasakian structures always coincide, obtaining a rank-based
classification. Furthermore, we prove a decomposition theorem for
these manifolds assuming the integrability of one of
the almost product structures. Finally, we show that the vertical distribution
is a minimum of the corrected energy.
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