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A REMARK ON H-CONTACT UNIT TANGENT SPHERE BUNDLES

  • Received : 2009.10.23
  • Published : 2011.03.01

Abstract

We shall give some curvature conditions for the unit tangent sphere bundle of an n($\geq$ 4)-dimensional Riemannian manifold to be H-contact. Furthermore, we provide an example illustrating Main Theorem.

Keywords

References

  1. A. L. Besse, Manifolds All of Whose Geodesics are Closed, Springer-Verlag, Berlin-New York, 1978.
  2. D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Birkhauser, Boston, Inc., Boston, MA, 2002.
  3. E. Boeckx and L. Vanhecke, Harmonic and minimal vector fields on tangent and unit tangent bundles, Differential Geom. Appl. 13 (2000), no. 1, 77-93. https://doi.org/10.1016/S0926-2245(00)00021-8
  4. E. Boeckx and L. Vanhecke, Unit tangent sphere bundles with constant scalar curvature, Czechoslovak Math. J. 51(126) (2001), no. 3, 523-544. https://doi.org/10.1023/A:1013779805244
  5. G. Calvaruso and D. Perrone, H-contact unit tangent sphere bundles, Rocky Mountain J. Math. 37 (2007), no. 5, 1435-1458. https://doi.org/10.1216/rmjm/1194275928
  6. P. Carpenter, A. Gray, and T. J. Willmore, The curvature of Einstein symmetric spaces, Quart. J. Math. Oxford Ser. (2) 33 (1982), no. 129, 45-64. https://doi.org/10.1093/qmath/33.1.45
  7. Y. D. Chai, S. H. Chun, J. H. Park, and K. Sekigawa, Remarks of Einstein unit tangent bundles, Monatsh. Math. 155 (2008), no. 1, 31-42. https://doi.org/10.1007/s00605-008-0534-4
  8. S. H. Chun, J. H. Park, and K. Sekigawa, H-contact unit tangent sphere bundles of Einstein manifolds, Quart. J. Math., (to appear), DOI:10.1093/qmath/hap025.
  9. P. Nurowski and M. Pruzanowski, A four-dimensional example of a Ricci flat metric admitting almost-Kahler non-Kahler structure, Classical Quantum Gravity 16 (1999), no. 3, L9-L13. https://doi.org/10.1088/0264-9381/16/3/002
  10. T. Oguro, K. Sekigawa, and A. Yamada, Four-dimensional almost Kahler Einstein and weakly *-Einstein manifolds, Yokohama Math. J. 47 (1999), no. 1, 75-92.
  11. J. H. Park and K. Sekigawa, When are the tangent sphere bundles of a Riemannian manifold $\eta$-Einstein?, Ann. Global Anal. Geom. 36 (2009), no. 3, 275-284. https://doi.org/10.1007/s10455-009-9160-1
  12. J. H. Park and K. Sekigawa, Notes on tangent sphere bundles of constant radii, J. Korean Math. Soc. 46 (2009), no. 6, 1255-1265. https://doi.org/10.4134/JKMS.2009.46.6.1255
  13. D. Perrone, Contact metric manifolds whose characteristic vector eld is a harmonic vector eld, Differential Geom. Appl. 20 (2004), no. 3, 367-378. https://doi.org/10.1016/j.difgeo.2003.12.007
  14. C. M. Wood, On the energy of a unit vector eld, Geom. Dedicata 64 (1997), no. 3, 319-330. https://doi.org/10.1023/A:1017976425512

Cited by

  1. H-contact unit tangent sphere bundles of Riemannian manifolds vol.49, 2016, https://doi.org/10.1016/j.difgeo.2016.09.002