Immersions into Statistical Manifolds

2018/03/07 by Mahesh, T V, Moosath, K S Subrahamanian
#53A15 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.02538

Abstract

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.

Related

• The Bonnet theorem for statistical manifolds
• Monotone invariants and embeddings of statistical manifolds
• Equiaffine Structure and Conjugate Ricci-symmetry of a Statistical Manifold
• Constancy of curvature and conformal-projective flatness of statistical manifolds
• Affine and Conformal Submersions with Horizontal Distribution and Statistical Manifolds