5 papers
Doubly Totally-Umbilical Statistical Submanifolds in the Probability Simplex
Ryu Ueno
We give a complete classification of doubly totally-umbilical submanifolds in the probability simplex. The probability simplex is one of the most standard statistical manifolds, an…
Geodesic Connectedness on Statistical Manifolds with Divisible Cubic Forms
Ryu Ueno
The class of statistical manifolds with divisible cubic forms arises from affine differential geometry. We examine the geodesic connectedness of affine connections on this class of…
Statistical Biharmonicity of Identity Maps
Ryu Ueno
The tension field of the identity map from a statistical manifold to a Riemannian statistical manifold, which shares the same Riemannian metric, is the Tchevychev vector field mult…
A Variation Problem for Mappings between Statistical Manifolds
Hitoshi Furuhata, Ryu Ueno
We present statistical biharmonic maps, a new class of mappings between statistical manifolds naturally derived from a variation problem. We give the Euler-Lagrange equation of thi…
The Second Variational Formula for Statistical Biharmonic Maps
Ryu Ueno
Recently, the statistical bi-energy functional and its first variational formula were introduced by the author and H. Furuhata. The Maps satisfying the corresponding Euler-Lagrange…