Geometry of Fisher Information Metric and the Barycenter Map

摘要: Geometry of Fisher metric and geodesics on a space probability measures defined compact manifold is discussed applied to geometry barycenter map associated with Busemann function an Hadamard \(X\). We obtain explicit formula geodesic then several theorems geodesics, one which asserts that any two can be joined by unique geodesic. Using thus obtained properties fibre structure geodesical each are discussed. Moreover, isometry problem \(X\) its ideal boundary \(\partial X\)—for given homeomorphism \(\Phi\) X\) find whose X\)-extension coincides \(\Phi\)—is investigated in terms the map.