In this note we show that all diffeomorphisms close enough to the time-one map of the frame flow on certain negatively curved manifolds are ergodic. As a simple corollary we deduce that the frame flows are ergodic for all compact manifolds with curvature pinched sufficiently close to -1, thus providing results in the case of manifolds of dimension 7 or 8 which were missing from the results of Brin and Karcher.
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Two problems related to this paper are included in the Bloomington Geometry Problem List.
Authors' addresses: Keith Burns Department of Mathematics Northwestern University Evanston, IL 60208-2730 Mark Pollicott Mathematics Institute University of Warwick Coventry CV4 7AL UK