The Canonical 8-form on Manifolds with Holonomy Group Spin(9)
| dc.contributor.author | Castrillón López, Marco | |
| dc.contributor.author | Martínez Gadea, Pedro | |
| dc.contributor.author | Mykytyuk, I.V. | |
| dc.date.accessioned | 2023-06-20T03:33:15Z | |
| dc.date.available | 2023-06-20T03:33:15Z | |
| dc.date.issued | 2010 | |
| dc.description.abstract | An explicit expression of the canonical 8-form on a Riemannian manifold with a Spin(9)-structure, in terms of the nine local symmetric involutions involved, is given. The list of explicit expressions of all the canonical forms related to Berger’s list of holonomy groups is thus completed. Moreover, some results on Spin(9)-structures as G-structures defined by a tensor and on the curvature tensor of the Cayley planes, are obtained. | |
| 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/21735 | |
| dc.identifier.doi | 10.1142/S0219887810004786 | |
| dc.identifier.issn | 0219-8878 | |
| dc.identifier.officialurl | http://www.worldscientific.com/toc/ijgmmp/07/07 | |
| dc.identifier.relatedurl | http://www.worldscientific.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/43849 | |
| dc.issue.number | 7 | |
| dc.journal.title | International Journal of Geometric Methods in Modern Physics | |
| dc.language.iso | eng | |
| dc.page.final | 1183 | |
| dc.page.initial | 1159 | |
| dc.publisher | World Scientific | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 514.762 | |
| dc.subject.keyword | Canonical 8-form on a Spin(9)-Manifold | |
| dc.subject.keyword | Curvature Tensor of the Cayley Planes | |
| dc.subject.keyword | Basic Spin Representation of Spin(9) | |
| dc.subject.ucm | Geometría diferencial | |
| dc.subject.unesco | 1204.04 Geometría Diferencial | |
| dc.title | The Canonical 8-form on Manifolds with Holonomy Group Spin(9) | |
| dc.type | journal article | |
| dc.volume.number | 7 | |
| dcterms.references | K. Abe, Closed regular curves and the fundamental form on the projective spaces,Proc. Japan Acad. Ser. A Math. Sci. 68 (1992), no. 6, 123–125. K. Abe and M. Matsubara, Invariant forms of the exceptional symmetric spaces FII and EIII, Transformation group theory (Taejon, 1996), 3–16, Korea Adv.Inst. Sci. Tech., Taejon. J. F. Adams, Lectures on exceptional Lie groups, Chicago Lectures in Mathematics, Chicago Univ. Press, 1996. D. V. Alekseevskiı, Riemannian spaces with non-standard holonomy groups, Funct. Anal. Appl. 2 (1968), 97–105. T. Banks, W. Fischler, S. H. Shenker, and L. Susskind, M theory as a matrix model: a conjecture, Phys. Rev. D (3) 55 (1997), no. 8, 5112–5128. M. Berger, Sur les groupes d'holonomie homogene des varietes a connexion affine et des varietes riemanniennes, Bull. Soc. Math. France 83 (1955), 279–330. Du cote de chez Pu, Ann. Sci. Ecole Norm. Sup. (4) 5 (1972), 1–44. D. Bernard, Sur la geometrie differentielle des G-structures, Ann. Inst. Fourier 10 (1960), 151–270. A. L. Besse, Manifolds all of whose geodesics are closed, Ergebnisse der Mathematik und ihrer Grenzgebiete, 93. Springer-Verlag, Berlin-New York, 1978. E. Bonan, Sur les varietes riemanniennes a groupe dholonomie G2 ou Spin(7), C. R. Acad. Sci. Paris Ser. I Math. 262 (1966), 127–129. C. Brada and F. Pecaut-Tison, Calcul explicite de la courbure et de la 8-forme canonique du plan projectif des octaves de Cayley, C. R. Acad. Sci. Paris Ser. I Math. 301 (1985), no. 2, 41–44. Geometrie du plan projectif des octaves de Cayley, Geom. Dedicata 23 (1987), no. 2, 131–154. R. B. Brown and A. Gray, Riemannian manifolds with holonomy group Spin(9),Diff. Geom. in honor of K. Yano, Kinokuniya, Tokyo, 1972, pp. 41–59. Th. Friedrich, Weak Spin(9)-structures on 16-dimensional Riemannian manifolds Asian J. Math. 5 (2001), no. 1, 129–160. Spin(9)-structures and connections with totally skew-symmetric torsion, J. Geom. Phys. 47 (2003), no. 2–3, 197–206. On types of non-integrable geometries, Proc. of the 22nd Winter School “Geometry and Physics” (Srn´ı, 2002). Rend. Circ. Mat. Palermo (2) Suppl. no.71 (2003), 99–113. A. Fujimoto, Theory of G-structures, Publ. Study Group Geom., vol. 1, Tokyo,1972. T. Hangan, On a formula relating projective and metric invariants on Grassmannians Conference on differential geometry on homogeneous spaces (Turin, 1983)Rend. Sem. Mat. Univ. Politec. Torino 1983, Special Issue, 61–73 (1984). R. Held, I. Stavrov, and B. Van Koten, (Semi)-Riemannian geometry and (para)octonionic projective planes, Differential Geom. Appl. 27 (2009), no. 4, 464–481 24 S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Academic Press, New York-San Francisco-London, 1978. N. Hitchin, Stable forms and special metrics, Contemp. Math. 288 (2001), 70–89. V. Y. Kraines, Topology of quaternionic manifolds, Bull. Amer. Math. Soc. 71(1965), 526–527. K.-H. Lam, Spectrum of the Laplacian on manifolds with Spin(9) holonomy,Math.Res. Lett. 15 (2008), no. 5–6, 1167–1186. D. Marın and M. de Leon, Classification of material G-structures, Mediterr. J.Math. 1 (2004), no. 4, 375–416. I. V. Mykytyuk, Kahler structures on tangent bundles of symmetric spaces of rank one (Russian), Mat. Sb. 192 (2001), no. 11, 93–122; translation in Sb. Math. 192 (2001), no. 11–12, 1677–1704. The triple Lie system of the symmetric space F4/Spin(9), Asian J. Math 6 (2002), no. 4, 713–718. M. Postnikov, Lie groups and Lie algebras, Lectures in Geometry. Semester V Translated from the Russian by Vladimir Shokurov. MIR, Moscow, 1986. S. Salamon, Riemannian geometry and holonomy groups, Longman Sci. & Tech.,Harlow, UK, 1989. H. Sati, OP2 bundles in M-theory, to appear in Commun. Number Theory Phys.arXiv:0807.4899. On the geometry of the supermultiplet in M-theory, arXiv:0909.4737. B. de Wit, A. K. Tollsten, and H. Nicolai, Locally supersymmetric D = 3 nonlinear sigma models, Nuclear Phys. B 392 (1993), no. 1, 3–38. F. Witt, Special metric structures and closed forms, Ph. D. Thesis, Univ. of Oxford, 2005. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 32e59067-ef83-4ca6-8435-cd0721eb706b | |
| relation.isAuthorOfPublication.latestForDiscovery | 32e59067-ef83-4ca6-8435-cd0721eb706b |
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