Homogeneous spin Riemannian manifolds with the simplest Dirac operator
Homogeneous spin Riemannian manifolds with the simplest Dirac operator
We investigate the existence of non-symmetric 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 expressionM = G/K and reductive decomposition g = k m. Using transversally symmetric fibrations of non-compact type, we give a large list of them.
The first and second authors have been supported by DGI (Spain) Project MTM2013-46961-P.
18 pags.; 4 tabs.; MSC 2010: 53C30, 53C35, 34L40.
Peer reviewed
Riemannian symmetric spaces, Dirac operator, Homogeneous spin Riemannian manifold, Traceless cyclic homogeneous Riemannian manifolds
Riemannian symmetric spaces, Dirac operator, Homogeneous spin Riemannian manifold, Traceless cyclic homogeneous Riemannian manifolds
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