On a class of Kähler manifolds whose geodesic flows are integrable

1995/09/20 by Kazuyoshi Kiyohara, Kiyohara, Kazuyoshi
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9509004

67 pages, AmSTeX 2.1

arxiv created 1995/09/20 · openalex publication_date 1995/09/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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