Flat connections and Wigner-Yanase-Dyson metrics
Jencova, Anna
arXiv, 0307057 / Harvested from arXiv
Text on arXiv
On the manifold of positive definite matrices, we investigate the existence of pairs of flat affine connections, dual with respect to a given monotone metric. The connections are defined either using the $\alpha$-embeddings and finding the duals with respect to the metric, or by means of contrast functionals. We show that in both cases, the existence of such a pair of connections is possible if and only if the metric is given by the Wigner-Yanase-Dyson skew information.
Publié le : 2003-07-28
Classification:  Mathematical Physics,  Mathematics - Differential Geometry,  53Z05 
@article{0307057,
     author = {Jencova, Anna},
     title = {Flat connections and Wigner-Yanase-Dyson metrics},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0307057}
}

Jencova, Anna. Flat connections and Wigner-Yanase-Dyson metrics. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0307057/