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Lagrangian foliations and Anosov symplectomorphisms on Kähler manifolds. (English) Zbl 1478.32077

Summary: 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.

MSC:

32Q15 Kähler manifolds
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
53B35 Local differential geometry of Hermitian and Kählerian structures
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