Abstract
Abstract We show the existence of nonsymmetric homogeneous spin Riemannian manifolds whose Dirac operator is like that on a Riemannian symmetric spin space. Such manifolds are exactly the homogeneous spin Riemannian manifolds (M, g) which are traceless cyclic with respect to some quotient expression M = G/K and reductive decomposition 𝔤 = 𝔨 ⊕ 𝔪. Using transversally symmetric fibrations of noncompact type, we give a list of them.
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