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GRAY CURVATURE IDENTITIES FOR ALMOST CONTACT METRIC MANIFOLDS

  • 발행 : 2010.05.01

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.

키워드

참고문헌

  1. R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49. https://doi.org/10.2307/1995057
  2. D. E. Blair, Contact Manifolds in Riemannian Geometry, Springer-Verlag, Berlin-New York, 1976.
  3. D. E. Blair, Riemannian geometry of Contact and Symplectic Manifolds, Progess in Mathematics, Birkhauser Boston, 2002.
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  5. W. M. Boothby and H. C. Wang, On contact manifolds, Ann. of Math. (2) 68 (1958), 721-734. https://doi.org/10.2307/1970165
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  8. A. Gray, Curvature identities for Hermitian and almost Hermitian manifolds, Tohoku Math. J. (2) 28 (1976), no. 4, 601-612. https://doi.org/10.2748/tmj/1178240746
  9. D. Janssens and L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. J. 4 (1981), no. 1, 1-27. https://doi.org/10.2996/kmj/1138036310
  10. R. S. Palais, A global formulation of the Lie theory of transformation groups, Mem. Amer. Math. Soc. No. 22 (1957), iii+123 pp.
  11. G. B. Rizza, Varieta parakahleriane, Ann. Mat. Pura Appl. (4) 98 (1974), 47-61. https://doi.org/10.1007/BF02414012
  12. F. Tricerri and L. Vanhecke, Curvature tensors on almost Hermitian manifolds, Trans. Amer. Math. Soc. 267 (1981), no. 2, 365-397. https://doi.org/10.2307/1998660
  13. L. Vanhecke, Almost Hermitian manifolds with J-invariant Riemann curvature tensor, Rend. Sem. Mat. Univ. Politec. Torino 34 (1975/76), 487-498.

피인용 문헌

  1. Riemannian submersions from almost contact metric manifolds vol.81, pp.1, 2011, https://doi.org/10.1007/s12188-011-0049-0