Non-existence of certain 3-structures

We introduce the notion of an epsilon-framed 3-structure. This is a general structure which includes many widely studied 3-structures (almost quaternion, almost contact, hyper f-structure, almost product, etc.). We prove the existence of Riemannian metrics compatible with such a structure. We also study particular cases of epsilon-framed 3-structures showing the non-existence of certain remarkable types of such structures. First, we prove the non-existence of P-Sasakian almost r-paracontact 3-structures. Then, we show the nonexistence of almost r-contact S-3-structures (with r > 1). Finally, we establish the non-existence of proper trans-Sasakian almost contact 3-structures. A consequence of this last result is that any b-Kenmotsu almost contact 3-structure must be hypercosymplectic.