Homogeneous Structures on Real and Complex Hyperbolic Spaces
| dc.contributor.author | Castrillón López, Marco | |
| dc.contributor.author | Martínez Gadea, Pedro | |
| dc.contributor.author | Swann, Andrew | |
| dc.date.accessioned | 2023-06-20T10:35:45Z | |
| dc.date.available | 2023-06-20T10:35:45Z | |
| dc.date.issued | 2009 | |
| dc.description.abstract | The connected groups acting by isometries on either the real or the complex hyperbolic spaces are determined. A Lie-theoretic description of the homogeneous Riemannian, respectively Kähler, structures of linear type on these spaces is then found. On both spaces, examples that are not of linear type are given. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/21797 | |
| dc.identifier.issn | 0019-2082 | |
| dc.identifier.officialurl | http://0-projecteuclid.org.cisne.sim.ucm.es/DPubS/Repository/1.0/Disseminate?handle=euclid.ijm/1266934792&view=body&content-type=pdfview_1 | |
| dc.identifier.relatedurl | http://ijm.math.illinois.edu/ | |
| dc.identifier.relatedurl | http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ijm | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50704 | |
| dc.issue.number | 2 | |
| dc.journal.title | Illinois Journal of Mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 574 | |
| dc.page.initial | 561 | |
| dc.publisher | University of Illinois | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 514.762 | |
| dc.subject.keyword | Homogeneous Structures | |
| dc.subject.keyword | Hyperbolic Spaces | |
| dc.subject.keyword | Isometry Group | |
| dc.subject.keyword | Iwasawa Decomposition | |
| dc.subject.ucm | Geometría diferencial | |
| dc.subject.unesco | 1204.04 Geometría Diferencial | |
| dc.title | Homogeneous Structures on Real and Complex Hyperbolic Spaces | |
| dc.type | journal article | |
| dc.volume.number | 53 | |
| dcterms.references | E. Abbena and S. Garbiero, Almost Hermitian homogeneous structures, Proc. Edinburgh Math. Soc. (2) 31 (1988), no. 3, 375-395. W. Ambrose and I. M. Singer, On homogeneous Riemannian manifolds, Duke Math. J. 25 (1958), 647-669. L. Bérard-Bergery, Les espaces homogènes riemanniens de dimension 4, Riemannian geometry in dimension 4 (Paris, 1978/1979), Textes Math., vol. 3, CEDIC, Paris, 1981, pp. 40-60. A. L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, vol. 10, Springer, Berlin, Heidelberg and New York, 1987. M. Castrillón López, P. M. Gadea, and A. F. Swann, Homogeneous quaternionic Kähler structures and quaternionic hyperbolic space, Transform. Groups 11(2006),no. 4, 575-608. P. M. Gadea, A. Montesinos Amilibia, and J. Muñoz Masqué, Characterizing the complex hyperbolic space by Kähler homogeneous structures, Math. Proc. Cambridge Philos. Soc. 128 (2000), no. 1, 87-94. V. V. Gorbatsevich, A. L. Onishchik, and E. B. Vinberg, Structure of Lie groups and Lie algebras, Lie groups and Lie algebras III (A. L. Onishchik and E. B.Vinberg, eds.), Encyclopaedia of Mathematical Sciences, vol. 41, Springer-Verlag, Berlin, 1994, pp. 1-248. M. Goto and H.-C. Wang, Non-discrete uniform subgroups of semisimple Lie groups, Math. Ann. 198 (1972), 259-286. S. Kobayashi and K. Nomizu, Foundations of diferential geometry. Volume II, Tracts in Mathematics, Number 15, Wiley, New York, 1969. K. Nomizu, Invariant ane connections on homogeneous spaces, Amer. J. Math.76 (1954), 33-65. A. M. Pastore, On the homogeneous Riemannian structures of type T1©T3, Geom. Dedicata 30 (1989), no. 2, 235-246. Canonical connections with an algebraic curvature tensor field on naturally reductive spaces, Geom. Dedicata 43 (1992), no. 3, 351-361. Homogeneous representations of the hyperbolic spaces related to homogeneous structures of class T1 © T3, Rend. Mat. Appl. (7) 12 (1992), no. 2, 445-453. A. M. Pastore and F. Verroca, Some results on the homogeneous Riemannian structures of class T1 © T2, Rend. Mat. Appl. (7) 11 (1991), no. 1, 105-121. K. Sekigawa, Notes on homogeneous almost Hermitian manifolds, Hokkaido Math.J. 7 (1978), no. 2, 206-213. F. Tricerri and L. Vanhecke, Homogeneous structures on Riemannian manifolds,London Mathematical Society Lecture Note Series, vol. 83, Cambridge University Press,Cambridge, 1983. D. Witte, Cocompact subgroups of semisimple Lie groups, Lie algebras and related topics. Proceedings of the conference held at the University of Wisconsin,Madison, Wisconsin, May 22-June 1, 1988 (Georgia Benkart and J. Marshall Osborn, eds.), Contemporary Mathematics, vol. 110, American Mathematical Society, Providence, RI, 1990, pp. 309-313. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 32e59067-ef83-4ca6-8435-cd0721eb706b | |
| relation.isAuthorOfPublication.latestForDiscovery | 32e59067-ef83-4ca6-8435-cd0721eb706b |
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