Immersions into Statistical Manifolds

T V Mahesh; K S Subrahamanian Moosath

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arXiv · 1803.02538

Immersions into Statistical Manifolds

T V Mahesh·K S Subrahamanian Moosath

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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.

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BibTeX RIS

T V Mahesh, K S Subrahamanian Moosath. 2018-03-07. Immersions into Statistical Manifolds. https://arxiv.org/abs/1803.02538

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