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Lagrangian foliations and Anosov symplectomorphisms on Kähler manifolds

Published online by Cambridge University Press:  30 October 2020

M. J. D. HAMILTON
Affiliation:
Institut für Geometrie und Topologie, Universität Stuttgart, Pfaffenwaldring 57, 70569Stuttgart, Germany (e-mail: mark.hamilton@math.lmu.de)
D. KOTSCHICK*
Affiliation:
Mathematisches Institut, LMU München, Theresienstr. 39, 80333München, Germany
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Abstract

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We investigate parallel Lagrangian foliations on Kähler manifolds. On the one hand, we show that a Kähler metric admitting a parallel Lagrangian foliation must be flat. On the other hand, we give many examples of parallel Lagrangian foliations on closed flat Kähler manifolds which are not tori. These examples arise from Anosov automorphisms preserving a Kähler form.

Type
Original Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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