Ergodic Rotations of Nilmanifolds Conjugate to Their Inverses

摘要

In answer to a question posed in cite{G}, we give sufficientconditions on a Lie nilmanifold so that any ergodic rotation of thenilmanifold is metrically conjugate to its inverse. The condition isthat the Lie algebra be what we call quasi-graded, and is weaker thanthe property of being graded. Furthermore, the conjugating map can bechosen to be an involution. It is shown that for a special class ofgroups, the condition of quasi-graded is also necessary. In certainexamples there is a continuum of conjugacies.