Immersions into Statistical Manifolds
Differential Geometry
2020-09-14 v3
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.
Keywords
Cite
@article{arxiv.1803.02538,
title = {Immersions into Statistical Manifolds},
author = {T V Mahesh and K S Subrahamanian Moosath},
journal= {arXiv preprint arXiv:1803.02538},
year = {2020}
}