Strongly degenerate homogeneous pseudo-Kähler structures of linear type and complex plane waves
| dc.contributor.author | Castrillón López, Marco | |
| dc.contributor.author | Luján, I | |
| dc.date.accessioned | 2023-06-19T13:22:36Z | |
| dc.date.available | 2023-06-19T13:22:36Z | |
| dc.date.issued | 2013-11 | |
| dc.description.abstract | We study the class K2+K4 of homogeneous pseudo-Kähler structures in the strongly degenerate case. The local form and the holonomy of a pseudo-Kähler manifold admitting such a structure are obtained, leading to a possible complex generalization of homogeneous plane waves. The same question is tackled in the case of pseudo-hyper-Kähler and pseudo-quaternion Kähler manifolds. | |
| 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.sponsorship | MINECO (Spain) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/23935 | |
| dc.identifier.doi | 10.1016/j.geomphys.2013.04.010 | |
| dc.identifier.issn | 0393-0440 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0393044013000995# | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/33413 | |
| dc.journal.title | Journal of geometry and physics | |
| dc.language.iso | eng | |
| dc.page.final | 19 | |
| dc.page.initial | 1 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | MTM2011-22528. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 515.122.4 | |
| dc.subject.keyword | Homogeneous plane waves | |
| dc.subject.keyword | Pseudo-hyper-Kähler | |
| dc.subject.keyword | Pseudo-Kähler | |
| dc.subject.keyword | Pseudo-quaternion Kähler | |
| dc.subject.keyword | Reductive homogeneous pseudo-Riemannian spaces | |
| dc.subject.ucm | Geometría diferencial | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1204.04 Geometría Diferencial | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Strongly degenerate homogeneous pseudo-Kähler structures of linear type and complex plane waves | |
| dc.type | journal article | |
| dc.volume.number | 73 | |
| dcterms.references | W. Ambrose, I.M. Singer, On homogeneous Riemannian manifolds, Duke Math. J. 25 (1958) 647–669. F. Tricerri, L. Vanhecke, Homogeneous Structures on Riemannian Manifolds, Cambridge University Press, Cambridge, 1983. S. Cecotti, Homogeneous Käahler manifolds and T-algebras in N=2 2 supergravity and superstrings, Comm. Math. Phys. 124 (1989) 23–55. B. de Wit, A. Van Proeyen, Special geometry, cubic polynomials and homogeneous quaternionic spaces, Comm. Math. Phys. 149 (1992) 307–333. B.K. Darian, H.P. Künzle, Cosmological Einstein-Yang-Mills equations, J. Math. Phys. 38 (9) (1997) 4696–4713. K.E. Osetrin, V.V. Obukhov, A.E. Filippov, Homogeneous spacetimes and separation of variables in the Hamilton-Jacobi equation, J. Phys. A 39 (21) (2006)6641–6647. M. Castrillón López, P.M. Gadea, A.F. Swann, Homogeneous quaternionic Kähler structures and quaternionic hyperbolic space, Transform. Groups 11 (4) (2006) 575–608. P.M. Gadea, A. Montesinos Amilibia, J. Mu~noz Masqué, Characterizing the complex hyperbolic space by Kähler homogeneous structures, Math. Proc. Cambridge Philos. Soc. 128 (1) (2000) 87–94. P. Meessen, Homogeneous Lorentzian spaces admitting a homogeneous structure of type T1+T3, J. Geom. Phys. 56 (2006) 754–761. A. Montesinos Amilibia, Degenerate homogeneous structures of type s1 pseudo-Riemannian manifolds, Rocky Mountain J. Math. 31 (2) (2001) 561–579. A. Galaev, Holonomy groups and special geometric structures of pseudo-Kählerian manifolds of index 2, Mathematisch-Naturwissenschaftliche Fakultat II (Dissertation), Berlin: Humboldt-Univ., Preprint: arXiv:math/0612392vl [math.DG], 2006. p. 135. P.M. Gadea, José A. Oubi~na, Reductive homogeneous pseudo-Riemannian manifolds, Monatsh. Math. 124 (1997) 17–34. V.F. Kiričenko, On homogeneous Riemannian spaces with an invariant structure tensor, Sov. Math. Dokl. 21 (1980) 734–737. W. Batat, P.M. Gadea, José A. Oubi~na, Homogeneous pseudo-Riemannian structures of linear type, J. Geom. Phys. 61 (2011) 745–764. S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, Volumes I & II, John Wiley & Sons, Inc. (Interscience Division), New York, 1963,1969. M. Brozos-Vázquez, E. García-Río, P. Gilkey, S. Nikčević, R. Vázquez-Lorenzo, The Geometry of Walker Manifolds, in: Synthesis Lectures on Mathematics and Statistics, vol. 5, Morgan & Claypool Publ., 2009. José M.M. Senovilla, Singularity theorems and their consequences, Gen. Relativity Gravitation 30 (5) (1998)701–848. W. Fulton, J. Harris, Representation Theory: A First Course, in: Graduate Text in Mathematics, vol. 129, Springer-Verlag, New York, 1991. M. Blau, M. O'Loughlin, Homogeneous plane waves, Nuclear Phys. B 654 (2003) 135–176. M. Cahen, N. Wallach, Lorentzian symmetric spaces, Bull. Amer. Math. Soc. 76 (1970) 585–591. M. Blau, M. Borunda, M. O'Loughlin, G. Papadopoulos, The universality of Penrose limits near space-time singularities, J. High Energy Phys. 0407 (2004) 068. hep-th/0403252. I. Kath, M. Olbrich, On the structure of pseudo-Riemannian symmetric spaces, Transform. Groups 14 (4) (2009) 847–885. J. Bicak, Selected solutions of Einstein's field equations: their role in general relativity and astrophysics, Lecture Notes in Phys. 540 (2000) 1–126. J. Ehlers, W. Kundt, Exact solutions of the gravitational field equations, in: L. Witten (Ed.), Gravitation: An Introduction to Current Research, Wiley, New York, 1962, pp. 49–101. D.V. Alekseevsky, V. Cortés, Classification of pseudo-Riemannian symmetric spaces of quaternionic Kähler type, Amer. Math. Soc. Transl. Ser. 2 213 (2005) 33–62. M. Castrillón López, I. Luján, Pseudo-hyper-Kähler and para-quaternion Kähler homogeneous structures, Preprint. A. Fino, Intrinsic torsion and weak holonomy, Math. J. Toyama Univ. 21 (1998) 1–22. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 32e59067-ef83-4ca6-8435-cd0721eb706b | |
| relation.isAuthorOfPublication.latestForDiscovery | 32e59067-ef83-4ca6-8435-cd0721eb706b |
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