Product of statistical manifolds with a non-diagonal metric

Year 2017, Volume: 5 Issue: 3, 308 - 321, 01.07.2017

Djelloul Djebbouri Seddik Ouakkas

https://izlik.org/JA57NG98RG

Abstract

Keywords

Warped product , dualistic structures

References

• Amari, S., Differential-geometrical Methods in statistics, Lecture Notes in statistics, 28, Springer, Berlin, 1985.55.
• S. Amari, H. Nagaoka, Methods of information geometry, Amer. Math.Soc., Providence; Oxford University Press, Oxford, 2000.
• J. K. Beem, P. E. Ehrlich and Th. G. Powell, Warped product manifolds in relativity, Selected Studies: Physics-astrophysics, mathematics, history of science, pp. 41-56, North-Holland, Amesterdam-New York, 1982.
• R. L. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1-49.
• Furuhata, H., Hypersurfaces in statistical manifolds, Diff. Geom. Appl., 27, 2009, 420-429.55.
• R. Nasri, Non-diagonal metric on a product riemannian manifold, arXiv: 1501.00308, 2015.
• R. Nasri and M. Djaa, Sur la courbure des variétés riemanniennes produits, Sciences et Technologie, A-24 (2006), 15-20.
• B. O’Neill, Semi-Riemannian geometry, Academic Press, New-York, 1983.
• Todjihounde, L., Dualistic structures on warped product manifolds, Diff. Geom.-Dyn. Syst. 8, (2006), 278-284.