Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T15:25:03.250Z Has data issue: false hasContentIssue false
  • English
  • Français

H-CONTACT UNIT TANGENT SPHERE BUNDLES OF FOUR-DIMENSIONAL RIEMANNIAN MANIFOLDS

Part of: Global differential geometry

Published online by Cambridge University Press:  21 September 2011

SUN HYANG CHUN ,
JEONGHYEONG PARK  and
KOUEI SEKIGAWA
SUN HYANG CHUN
Affiliation:
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea (email: [email protected])
JEONGHYEONG PARK*
Affiliation:
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea (email: [email protected])
KOUEI SEKIGAWA
Affiliation:
Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the geometric properties of a base manifold whose unit tangent sphere bundle, equipped with the standard contact metric structure, is H-contact. We prove that a necessary and sufficient condition for the unit tangent sphere bundle of a four-dimensional Riemannian manifold to be H-contact is that the base manifold is 2-stein.

Keywords

tangent sphere bundleH-contact manifold2-stein

MSC classification

Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 2 , October 2011 , pp. 243 - 256
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The research of S. H. Chun was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2009-351-C00010). The research of J. H. Park was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0028097).

References

[1]Blair, D. E., Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics, 203 (Birkhäuser, Boston, 2002).CrossRefGoogle Scholar
[2]Boeckx, E. and Vanhecke, L., ‘Harmonic and minimal vector fields in tangent and unit tangent bundles’, Differential Geom. Appl. 13 (2000), 77–93.CrossRefGoogle Scholar
[3]Boeckx, E. and Vanhecke, L., ‘Unit tangent sphere bundles with constant scalar curvature’, Czechoslovak Math. J. 51 (2001), 523–544.CrossRefGoogle Scholar
[4]Calvaruso, G. and Perrone, D., ‘H-contact unit tangent sphere bundles’, Rocky Mountain J. Math. 37 (2007), 1435–1458.CrossRefGoogle Scholar
[5]Calvaruso, G. and Perrone, D., ‘Homogeneous and H-contact unit tangent sphere bundles’, J. Aust. Math. Soc. 88 (2010), 323–337.CrossRefGoogle Scholar
[6]Carpenter, P., Gray, A. and Willmore, T. J., ‘The curvature of Einstein symmetric spaces’, Q. J. Math. Oxford 33 (1982), 45–64.CrossRefGoogle Scholar
[7]Chun, S. H., Park, J. H. and Sekigawa, K., ‘H-contact unit tangent sphere bundles of Einstein manifolds’, Q. J. Math. 62 (2011), 59–69.CrossRefGoogle Scholar
[8]Park, J. H. and Sekigawa, K., ‘When are the tangent sphere bundles of a Riemannian manifold η-Einstein?’, Ann. Global Anal. Geom. 36 (2009), 275–284.CrossRefGoogle Scholar
[9]Perrone, D., ‘Contact metric manifolds whose characteristic vector field is a harmonic vector field’, Differential Geom. Appl. 20 (2004), 367–378.CrossRefGoogle Scholar
[10]Wood, C. M., ‘On the energy of a unit vector field’, Geom. Dedicata 64 (1997), 319–330.CrossRefGoogle Scholar