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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]
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Abstract

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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).

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