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Advances in Geometry

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Volume 18, Issue 3


Homogeneous spin Riemannian manifolds with the simplest Dirac operator

P. M. Gadea / J. C. González-Dávila
  • Departamento de Matemáticas, EstadĂ­stica e InvestigaciĂłn Operativa, Universidad de La Laguna, 38200-La Laguna, Tenerife, Spain
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/ J. A. Oubiña
  • Departamento de XeometrĂ­a e TopoloxĂ­a, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782-Santiago de Compostela, Spain
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Published Online: 2018-04-05 | DOI: https://doi.org/10.1515/advgeom-2018-0003


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.

Keywords: Homogeneous (spin) Riemannian manifold; Dirac operator

MSC 2010: 53C30; 53C35; 34L40


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About the article

Received: 2016-02-08

Revised: 2016-05-24

Published Online: 2018-04-05

Published in Print: 2018-07-26

Funding: The first and second authors have been supported by DGI (Spain) Project MTM2013-46961-P.

Citation Information: Advances in Geometry, Volume 18, Issue 3, Pages 289–302, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2018-0003.

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