Homogeneous spin Riemannian manifolds with the simplest Dirac operator

2015/04/22 by P. M. Gadea, Gadea, P. M., J. C. González-Dávila +3
Mathematics · Physics and Astronomy · #34L40 (Secondary) #53C30 (Primary) #53C35 #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1504.05925

openalex publication_date 2015/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \mathfrakg = \mathfrakk ⊕ \mathfrakm. Using transversally symmetric fibrations of noncompact type, we give a list of them.

Related

• Cyclic homogeneous Riemannian manifolds
• Harmonic spinors on homogeneous spaces
• The symmetry of Spin^c Dirac spectrums on Riemannian product manifolds
• Dirac eigenspinors for generic metrics
• Some Conformally Flat Spin Manifolds, Dirac Operators and Automorphic Forms