International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 3, Pages 183-195
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 Vasile Oproiu. 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.
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.