Geodesic
Ergodic Rotations of Nilmanifolds Conjugate to Their Inverses
Canadian mathematical bulletin, Tome 44 (2001) no. 4, pp. 429-439

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In answer to a question posed in [3], we give sufficient conditions on a Lie nilmanifold so that any ergodic rotation of the nilmanifold is metrically conjugate to its inverse. The condition is that the Lie algebra be what we call quasi-graded, and is weaker than the property of being graded. Furthermore, the conjugating map can be chosen to be an involution. It is shown that for a special class of groups, the condition of quasi-graded is also necessary. In certain examples there is a continuum of conjugacies.
DOI : 10.4153/CMB-2001-043-2
Mots-clés : 28Dxx, 22E25 
Henniger, J. P. Ergodic Rotations of Nilmanifolds Conjugate to Their Inverses. Canadian mathematical bulletin, Tome 44 (2001) no. 4, pp. 429-439. doi: 10.4153/CMB-2001-043-2
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     title = {Ergodic {Rotations} of {Nilmanifolds} {Conjugate} to {Their} {Inverses}},
     journal = {Canadian mathematical bulletin},
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     year = {2001},
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     doi = {10.4153/CMB-2001-043-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-043-2/}
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