Immersions into Statistical Manifolds

摘要

This paper studies the geometry of immersions into statistical manifolds. A necessary and sufficient condition is obtained for statistical manifold structures to be dual to each other for a non-degenerate equiaffine immersion. Then, we obtain conditions for realizing an n-dimensional statistical manifold in an (n + 1)-dimensional statistical manifold and its converse. Centro-affine immersion of codimension two into a dually flat statistical manifold is defined. Also, we have shown that statistical manifold realized in a dually flat statistical manifold of codimension two is conformally-projectively flat.