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The Quarterly Journal of Mathematics Advance Access published online on July 31, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/hap025
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© 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

H-CONTACT UNIT TANGENT SPHERE BUNDLES OF EINSTEIN MANIFOLDS

Sun Hyang Chun {dagger} and Jeong Hyeong Park{ddagger}

Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea

Kouei Sekigawa §

Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan

{ddagger} Corresponding author. E-mail: parkj{at}skku.edu

Received 4 May 2009; revised 28 June 2009
  Abstract

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 shall prove that a necessary and sufficient condition for the unit tangent sphere bundle of an Einstein manifold to be H-contact is that the base manifold is 2-stein. As its applications, we give an explicit classification of such base manifolds in the special cases of irreducible symmetric spaces or of Kähler–Einstein manifolds with non-negative sectional curvature. Further, we provide examples illustrating the non-homogeneous situations in dimension four.

{dagger} E-mail: cshyang@skku.edu

§ E-mail: sekigawa@math.sc.niigata-u.ac.jp


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