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On a class of Kähler manifolds whose geodesic flows are integrable

Kazuyoshi Kiyohara
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Abstract

We study $n$-dimensional Kähler manifolds whose geodesic flows possess $n$ first integrals in involution that are fibrewise hermitian forms and simultaneously normalizable. Under some mild assumption, one can associate with such a manifold an $n$-dimensional commutative Lie algebra of infinitesimal automorphisms. This, combined with the given $n$ first integrals, makes the geodesic flow integrable. If the manifold is compact, then it becomes a toric variety.

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BibTeXRIS

Kazuyoshi Kiyohara. 1995-09-20. On a class of Kähler manifolds whose geodesic flows are integrable. https://arxiv.org/abs/dg-ga/9509004

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