Conjugate connections play a crucial role in information geometry.
For dually flat statistical spaces, we have the exponential and mixture connections that are dual to each other.
There have been several ways to define what we mean by a statistical manifold.
The following paper summarizes the various approaches nicely.
Conjugate connections on statistical manifolds
S. E. Stepanov, E. S. Stepanova and I. G. Shandra
It refers to a 1945 russian paper examining dual connections.
A. P. Norden,
On Pairs of Conjugate Parallel Displacements in Multidimensional Spaces,
Dokl. Akad. Nauk SSSR 49 (9), 1345-1347 (1945).
BTW, mathnet.ru is pretty good for finding Russian math papers. Search for Norden gives 72 results, all of them seem to be available as pdf's. This paper looks similar to the one cited, "Parallel Transport of Dual Vectors"
From : Yaroslav Bulatov @ 2010-10-19 03:53:57 Edit
Excellent. One more reason to get russian basics. Thanks for the link. Frank.
From : Frank @ 2010-10-19 19:49:03 Edit
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