Reduction of Homogeneous Pseudo-Kähler Structures by One-Dimensional Fibers
| dc.contributor.author | Carmona Jiménez, J. L. | |
| dc.contributor.author | Castrillón López, Marco | |
| dc.date.accessioned | 2023-06-17T08:29:57Z | |
| dc.date.available | 2023-06-17T08:29:57Z | |
| dc.date.issued | 2020-08-01 | |
| dc.description.abstract | We study the reduction procedure applied to pseudo-Kähler manifolds by a one dimensional Lie group acting by isometries and preserving the complex tensor. We endow the quotient manifold with an almost contact metric structure. We use this fact to connect pseudo-Kähler homogeneous structures with almost contact metric homogeneous structures. This relation will have consequences in the class of the almost contact manifold. Indeed, if we choose a pseudo-Kähler homogeneous structure of linear type, then the reduced, almost contact homogeneous structure is of linear type and the reduced manifold is of type C5⊕C6⊕C12 of Chinea-González classification. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/75547 | |
| dc.identifier.doi | 10.3390/axioms9030094 | |
| dc.identifier.issn | 2075-1680 | |
| dc.identifier.officialurl | https://doi.org/10.3390/axioms9030094 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/7296 | |
| dc.journal.title | Axioms | |
| dc.language.iso | eng | |
| dc.publisher | MDPI | |
| dc.rights | Atribución 3.0 España | |
| dc.rights.accessRights | open access | |
| dc.rights.uri | https://creativecommons.org/licenses/by/3.0/es/ | |
| dc.subject.cdu | 512 | |
| dc.subject.keyword | Ambrose–Singer connections | |
| dc.subject.keyword | almost contact metric manifolds | |
| dc.subject.keyword | homogeneous manifolds | |
| dc.subject.keyword | homogeneous structures | |
| dc.subject.keyword | pseudo-Kähler manifolds | |
| dc.subject.keyword | pseudo-Riemannian metric | |
| dc.subject.ucm | Álgebra | |
| dc.subject.unesco | 1201 Álgebra | |
| dc.title | Reduction of Homogeneous Pseudo-Kähler Structures by One-Dimensional Fibers | |
| dc.type | journal article | |
| dcterms.references | 1. Ambrose, W.; Singer, I.M. On homogeneous Riemannian manifolds. Duke Math. J. 1958, 25, 647–669. 2. Kiricenko, V.F. On homogeneous Riemannian spaces with an invariant structure tensor. Sov. Math. Dokl. 1980, 21, 734–737. 3. Tricerri, F.; Tricerri, G.; Vanhecke, L. Homogeneous Structures on Riemannian Manifolds, 1st ed.; Lon. Math. Soc. Lecture Notes Series 83; Cambridge University Press: London, UK, 1983. 4. Abbena, E.; Garbiero, S. Almost hermitian homogeneous structures. Proc. Edinb. Math. Soc. 1988, 31, 375–395. 5. Calvaruso, G.; Castrillón López, M. Pseudo-Riemannian Homogeneous Structures, 1st ed.; Developments in Mathematics 59; Springer: New York, NY, USA, 2019. 6. Castrillón López, M.; Luján, I. Homogeneous structures of linear type on e-Kähler and e- quaternion Kähler manifolds Rev. Mat. Iberoam. 2017, 33, 139–168. 7. Castrillón López, M.; Luján, I. Reduction of homogeneous Riemannian structures. Proc. Edinh. Math. Soc. 2015, 58, 81–106. 8. Chinea, D.; González, C. A Classification of Almost Contact Metric Manifolds. Annali di Matematica Pura ed Applicata 1990, 156, 15–36. 9. Batat, W.; Gadea, P.; Oubiña, J.A. Homogeneous pseudo-Riemannian structures of linear type. J. Geom. Phys. 2011, 60, 745–764. 10. Carmona Jiménez, J.L.; Castrillón López, M. The Ambrose-Singer theorem for general homogeneous spaces with applications to symplectic geometry. arXiv 2020, unpublished. Available online: https://arxiv.org/abs/2001.06254 (accessed on 17 January 2020). 11. Luján. I. Reductive locally homogeneous pseudo-Riemannian manifolds and Ambrose–Singer connections. Diff. Geom. Appl. 2015, 41, 65–90. 12. Blair, D.E. Riemannian Geometry of Contact and Symplectic Manifolds, 1st ed.; Progress in Mathematics 203; Birkhäuser: Basel, Switzerland, 2002. 13. Marsden, J.E.; Ostrowski, J. Symmetries in motion: Geometric foundations of motion control.Nonlinear Sci. Today 1996, 1–21. 14. Palais, R. A Global Formulation of the Lie Theory of Transformation Groups; Mem. Amer. Math. Soc. 22; American Mathematical Society: Providence, RI, USA, 1957. 15. Meessen, P. Homogeneous Lorentzian spaces admitting a homogeneous structure of type T1 + T2. J. Geom. Phys. 2006, 56, 754–761. 16. Castrillón López, M.; Luján, I. Strongly degenerate homogeneous pseudo-Kähler structures of linear type and complex plane waves. J. Geom. Phys. 2013, 73, 1–19. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 32e59067-ef83-4ca6-8435-cd0721eb706b | |
| relation.isAuthorOfPublication.latestForDiscovery | 32e59067-ef83-4ca6-8435-cd0721eb706b |
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