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( h , Φ ) -entropy differential metric

María Luisa Menéndez, Domingo Morales, Leandro Pardo, Miquel Salicrú (1997)

Applications of Mathematics

Burbea and Rao (1982a, 1982b) gave some general methods for constructing quadratic differential metrics on probability spaces. Using these methods, they obtained the Fisher information metric as a particular case. In this paper we apply the method based on entropy measures to obtain a Riemannian metric based on ( h , Φ ) -entropy measures (Salicrú et al., 1993). The geodesic distances based on that information metric have been computed for a number of parametric families of distributions. The use of geodesic...

∇-flat functions on manifolds

Wojciech Kozłowski (2004)

Annales Polonici Mathematici

We investigate ∇-flat and pointwise-∇-flat functions on affine and Riemannian manifolds. We show that the set of all ∇-flat functions on (M,∇) is a ring which has interesting properties similar to the ring of polynomial functions.

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