Curvature properties of 3-$$(\alpha ,\delta )$$-Sasaki manifolds

Abstract We investigate curvature properties of 3- $$(\alpha ,\delta )$$ ( α , δ ) -Sasaki manifolds, a special class almost 3-contact metric manifolds generalizing 3-Sasaki (corresponding to $$\alpha =\delta =1$$ = 1 ) that admit canonical connection with skew torsion and define Riemannian submersion over quaternionic Kähler manifold vanishing, positive or negative scalar curvature, according $$\delta =0$$ 0 , \delta >0$$ > <0$$ < . shall both the connection, particular focus on their operators, regarded as symmetric endomorphisms space 2-forms. describe spectrum, find distinguished eigenforms, study conditions strongly definite in sense Thorpe.