2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152074We 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.67 pages, AmSTeX 2.1Differential Geometrytext