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2013 | 11 | 1 | 149-160

Tytuł artykułu

On the characteristic connection of gwistor space

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Języki publikacji

EN

Abstrakty

EN
We give a brief presentation of gwistor spaces, which is a new concept from G 2 geometry. Then we compute the characteristic torsion T c of the gwistor space of an oriented Riemannian 4-manifold with constant sectional curvature k and deduce the condition under which T c is ∇c-parallel; this allows for the classification of the G 2 structure with torsion and the characteristic holonomy according to known references. The case of an Einstein base manifold is envisaged.

Wydawca

Czasopismo

Rocznik

Tom

11

Numer

1

Strony

149-160

Opis fizyczny

Daty

wydano
2013-01-01
online
2012-10-24

Twórcy

  • Departamento de Matemática da Universidade de Évora and Centro de Investigação em Matemática e Aplicações (CIMA-UÉ)

Bibliografia

  • [1] Abbassi M.T.K., Kowalski O., On Einstein Riemannian g-natural metrics on unit tangent sphere bundles, Ann. Global Anal. Geom., 2010, 38(1), 11–20 http://dx.doi.org/10.1007/s10455-010-9197-1
  • [2] Agricola I., The Srní lectures on non-integrable geometries with torsion, Arch. Math. (Brno), 2006, 42(suppl.), 5–84
  • [3] Albuquerque R., On the G 2 bundle of a Riemannian 4-manifold, J. Geom. Phys., 2010, 60(6–8), 924–939 http://dx.doi.org/10.1016/j.geomphys.2010.02.009
  • [4] Albuquerque R., Homotheties and topology of tangent sphere bundles, preprint available at http://arxiv.org/abs/1012.4135
  • [5] Albuquerque R., Salavessa I., The G 2 sphere of a 4-manifold, Monatsh. Math., 2009, 158(4), 335–348 http://dx.doi.org/10.1007/s00605-008-0053-3
  • [6] Albuquerque R., Salavessa I., Erratum to: The G 2 sphere of a 4-manifold, Monatsh. Math., 2010, 160(1), 109–110 http://dx.doi.org/10.1007/s00605-010-0191-2
  • [7] Arvanitoyeorgos A., SO(n)-invariant Einstein metrics on Stiefel manifolds, In: Differential Geometry and Applications, Brno, August 28–September 1, 1995, Masaryk University, Brno, 1996, 1–5
  • [8] Baum H., Friedrich Th., Grunewald R., Kath I., Twistors and Killing Spinors on Riemannian Manifolds, Teubner-Texte Math., 124, Teubner, Stuttgart, 1991
  • [9] Besse A.L., Einstein Manifolds, Ergeb. Math. Grenzgeb., 10, Springer, Berlin, 1987
  • [10] Blair D.E., Riemannian Geometry of Contact and Symplectic Manifolds, Progr. Math., 203, Birkhaüser, Boston, 2002
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  • [12] Boyer Ch.P., Galicki K., Matzeu P., On eta-Einstein Sasakian geometry, Comm. Math. Phys., 2006, 262(1), 177–208 http://dx.doi.org/10.1007/s00220-005-1459-6
  • [13] Boyer Ch.P., Galicki K., Nakamaye M., Einstein metrics on rational homology 7-spheres, Ann. Inst. Fourier (Grenoble), 2002, 52(5), 1569–1584 http://dx.doi.org/10.5802/aif.1925
  • [14] Bryant R.L., Some remarks on G 2 structures, In: Proceedings of Gökova Geometry-Topology Conference, Gökova, May 24–28, 2004, May 30–June 3, 2005, Gökova Geometry/Topology Conference, Gökova/International Press, Somerville, 2006
  • [15] Chai Y.D., Chun S.H., Park J.H., Sekigawa K., Remarks on η-Einstein unit tangent bundles, Monatsh. Math., 2008, 155(1), 31–42 http://dx.doi.org/10.1007/s00605-008-0534-4
  • [16] Chiossi S.G., Swann A., G 2-structures with torsion from half-integrable nilmanifolds, J. Geom. Phys., 2005, 54(3), 262–285 http://dx.doi.org/10.1016/j.geomphys.2004.09.009
  • [17] Fernández M., Gray A., Riemannian manifolds with structure group G 2, Ann. Mat. Pura Appl., 1982, 132, 19–45 http://dx.doi.org/10.1007/BF01760975
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  • [21] Friedrich Th., Kath I., 7-dimensional compact Riemannian manifolds with Killing spinors, Comm. Math. Phys., 1990, 133(3), 543–561 http://dx.doi.org/10.1007/BF02097009
  • [22] Kath I., Pseudo-Riemannian T-duals of compact Riemannian homogeneous spaces, Transform. Groups, 2000, 5(2), 157–179 http://dx.doi.org/10.1007/BF01236467
  • [23] Kobayashi S., Nomizu K., Foundations of Differential Geometry I, Interscience, New York-London, 1963
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  • [26] Wang Mc.Y., Ziller W., On normal homogeneous Einstein manifolds, Ann. Sci. École Norm. Sup., 1985, 18(4), 563–633

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Bibliografia

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