부산대학교 도서관

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