Abstract

July 1 - 15.50-16.20
A. Cena - Christoffel symbols of the alpha-connections on the alpha-bundles over the Exponential Statistical Manifolds.

Gibilisco and Pistone (1998) show that the pretangent and the tangent bundle over the Exponential Statistical Manifold are the natural domains to define, respectively, the mixture and the exponential connection in the non-parametric case. Then they define the infinite-dimensional version of the alpha-connections on a suitable family of vector bundles.
In this context we evaluate the Christoffel symbols of the exponential and mixture connection. After studying the regularity of the sphere in the Lebesgue spaces and the natural connection on its tangent bundle, we are able to give the Christoffel symbols of the alpha-connections. [an error occurred while processing this directive]