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International Journal of Mathematics and Mathematical Sciences
Volume 25, Issue 3, Pages 183-195
http://dx.doi.org/10.1155/S0161171201002009

A Kähler Einstein structure on the tangent bundle of a space form

Faculty of Mathematics, University Al. I. Cuza, Iaşi, Romania

Received 18 September 1998

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We obtain a Kähler Einstein structure on the tangent bundle of a Riemannian manifold of constant negative curvature. Moreover, the holomorphic sectional curvature of this Kähler Einstein structure is constant. Similar results are obtained for a tube around zero section in the tangent bundle, in the case of the Riemannian manifolds of constant positive curvature.