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On a Constant Curvature Statistical Manifold by Kobayashi, Shimpei; Ohno, Yu is a scholarly article available to read on EtoBox.

What is On a Constant Curvature Statistical Manifold about?

We will show that a statistical manifold $(M, g, \nabla)$ has a constant curvature if and only if it is a projectively flat conjugate symmetric manifold, that is, the affine connection $\nabla$ is projectively flat and the curvatures satisfies $R=R^*$, where $R^*$ is the curvature of the dual connection $\nabla^*$. Moreover, we will show that properly convex structures on a projectively flat compact manifold induces constant curvature $-1$ statistical structures and vice versa.

Author

Kobayashi, Shimpei; Ohno, Yu

Published

2020

Language

EN