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GRAY CURVATURE IDENTITIES FOR ALMOST CONTACT METRIC MANIFOLDS

Raluca Mocanu|Marian Ioan Munteanu
대한수학회 (The Korean Mathematical Society)|2010.05|대한수학회지 (Journal of the KMS)|제47권 제3호|pp. 505-521

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키워드

Sasakian manifoldsalmost Hermitian manifoldsalmost contact metric manifoldscurvature identitiesBoothby-Wang fibrationcone metriccosymplectic manifoldsgeneralized Heisenberg group
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초록

Alfred Gray introduced in [8] three curvature identities for the class of almost Hermitian manifolds. Using the warped product construction and the Boothby-Wang fibration we will give an equivalent of these identities for the class of almost contact metric manifolds.

Abstract

Alfred Gray introduced in [8] three curvature identities for the class of almost Hermitian manifolds. Using the warped product construction and the Boothby-Wang fibration we will give an equivalent of these identities for the class of almost contact metric manifolds.

참고문헌 (13)

  1. R. L. Bishop, "Manifolds of negative curvature", Trans. Amer. Math. Soc., 145, pp.1~49 (1969)
  2. D. E. Blair, "Contact Manifolds in Riemannian Geometry" (1976), Springer-Verlag
  3. D. E. Blair, "Riemannian geometry of Contact and Symplectic Manifolds" (2002), Progess in Mathematics
  4. A. Bonome, "On the classes of almost Hermitian structures on the tangent bundle of an almost contact metric manifold", Acta Math. Hungar., 56(1), pp.29~37 (1990)
  5. W. M. Boothby, "On contact manifolds", Ann. of Math., 68, pp.721~734 (1958)
  6. M. Fern´andez, "Nearly hypo structures and compact nearely K¨ahler 6-manifolds with conical singularities", J. London Math. Soc., 78(3), pp.580~604 (2008)
  7. J. C. Gonzalez, "Quasi-Sasakian homogeneous structures on the generalized Heisenberg group H(p, 1)", J. London Math. Soc., 105(1), pp.173~184 (1989)
  8. A. Gray, "Curvature identities for Hermitian and almost Hermitian manifolds", Tˆohoku Math. J., 28(4), pp.601~612 (1976)
  9. D. Janssens, "Almost contact structures and curvature tensors", Kodai Math. J., 4(1), pp.1~27 (1981)
  10. R. S. Palais, "A global formulation of the Lie theory of transformation groups", Mem. Amer. Math. Soc., (22), pp.111~123 (1957)
  11. G. B. Rizza, "Variet`a parak¨ahleriane", Ann. Mat. Pura Appl., 98(4), pp.47~61 (1974)
  12. F. Tricerri, "Curvature tensors on almost Hermitian manifolds", Trans. Amer. Math. Soc., 267(2), pp.365~397 (1981)
  13. L. Vanhecke, "Almost Hermitian manifolds with J-invariant Riemann curvature tensor", Rend. Sem. Mat. Univ. Politec. Torino, 34, pp.487~498 (1975)

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