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Ergodic Rotations of Nilmanifolds Conjugate to Their Inverses

Published online by Cambridge University Press:  20 November 2018

J. P. Henniger
J. P. Henniger*
Affiliation:
Department of Mathematics Trent University Peterborough, Ontario K9J 7B8, email: jhenniger@trentu.ca
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Abstract

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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.

Keywords

28Dxx22E25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 4 , 01 December 2001 , pp. 429 - 439
Copyright
Copyright © Canadian Mathematical Society 2001

References

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