Kazuyoshi Kiyohara

Two-dimensional geodesic flows having first integrals of higher degree

Abstract. We present a family of riemannian metrics on two-sphere having the property that the geodesic flows admit first integrals which are fiberwise homogeneous polynomials of degree greater than 2. They also have the property that all geodesics are closed.

On Liouville integrability of h-projectively equivalent Kähler metrics

Under a nondegeneracy condition we classify the compact connected Kahler manifolds admitting pairs of h-projectively equivalent metrics. Any such manifold is biholomorphically equivalent to ℂP n and has integrable geodesic flow.