Dual Affine Connections and Dually Flat Manifold

  • Shun-ichi AmariEmail author
Part of the Applied Mathematical Sciences book series (AMS, volume 194)


We have considered one affine connection, namely the Levi–Civita connection, in a Riemannian manifold M. However, we can establish a new edifice of differential geometry, by treating a pair of affine connections which are dually coupled with respect to the Riemannian metric.

Copyright information

© Springer Japan 2016

Authors and Affiliations

  1. 1.Brain Science InstituteRIKENWakoJapan

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