J Austral Math Soc Ser A 50 pp189--196, 1991.
(Received 12 December 1988; revised 18 September 1989)
In the first paper of this series we studied on a compact regular contact manifold the integral of the Ricci curvature in the direction of the characteristic vector field considered as a functional on the set of all associated metrics. We showed that the critical points of this functional are the metrics for which the characteristic vector field generates a 1-parameter group of isometries and conjectured that the result might be true without the regularity of the conract structure. In the present paper we show that this conjecture is false by studying this problem on the tangent sphere bundle of a Riemannian manifold. In particular the standard associated metric is a critical point if and only if the base manifold is of constant curvature +1 or -1; in the latter case the characteristic vector field does not generate a 1-parameter group of isometries.
1980 AMS Subject Classification (1985 Revision): 58E11, 53C15
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