Subtangent-like statistical manifolds
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Abstract
Subtangent-like statistical manifolds are introduced and characterization theorems for them are given. The special case when the conjugate connections are projectively (or dual-projectively) equivalent is considered.
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How to Cite
Blaga, A.
(2014).
Subtangent-like statistical manifolds.
Acta Mathematica Universitatis Comenianae, 83(1), 147-156.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/85/41
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References
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[15] H. Furuhata, Hypersurfaces in statistical manifolds, Differential Geometry and its Applications 27, 420-429, 2009.
[16] K. Takano, Statistical manifolds with almost complex structures, Tensor, N. S. 72 (3), 225-231, 2010.
[17] I. Vaisman, Lagrange geometry on tangent manifolds, Int. J. Math. Math. Sci. 51, 3241-3266, 2003.
[2] S. Amari, Dierential geometry of a parametric family of invertible linear systems Riemannian metric, dual ane connections and divergence, Math. Systems Theory 20, 53-82, 1987.
[3] S. Amari; H. Nagaoka, Methods of Information Geometry, Transl. Math. Monogr. 191, Oxford University Press, Oxford, 2000.
[4] O. Calin; H. Matsuzoe, J. Zhang, Generalizations of conjugate connections, Trends in differential geometry, complex analysis and mathematical physics, World Sci. Publ., Hackensack, NJ, 26-34, 2009.
[5] R. S. Clark; M. Bruckheimer, Sur les estructures presque tangents, C. R. Acad. Sci. Paris Ser. I Math. 251, 627-629, 1960.
[6] R. S. Clark; M. Bruckneimer, Tensor structures on a
differentiable manifold, Annali di Matematica pure ed applicata 54, 123-142, 1961.
[7] M. Crasmareanu, Nonlinear connections and semisprays on tangent manifolds, Novi Sad J. Math. 33 (2), 11-22, 2003.
[8] C. T. J. Dodson, Spatial statistical and information geometry for parametric statistical models of galaxy clustering, Int. J. Theor. Phys. 38 (10), 1999.
[9] T. Li; L. Peng; H. Sun, The geometric structure of the inverse gamma distribution, Beitrage Algebra Geom. (Contributions to Algebra and Geometry) 49, 217-225, 2008.
[10] A. Norden, Anely Connected Spaces, GRMFL, Moscow, 1976.
[11] K. Nomizu, Ane connections and their use, Geometry and Topology of Submanifolds VII, ed. F. Dillen, World Scientic, 1995.
[12] H. Matsuzoe, Statistical manifolds and its generalization, Proceedings of the 8th International Workshop on Complex Structures and Vector Fields, World Scientic, 2007.
[13] S. Ivanov, On dual-projectively at ane connections, J. Geom. 53 (1), 89-99, 1995.
[14] H. A. Eliopoulos, Structures presque tangents sur les varietes dierentiables, C. R. Acad. Sci. Paris Ser. I Math. 255, 1563-1565, 1962.
[15] H. Furuhata, Hypersurfaces in statistical manifolds, Differential Geometry and its Applications 27, 420-429, 2009.
[16] K. Takano, Statistical manifolds with almost complex structures, Tensor, N. S. 72 (3), 225-231, 2010.
[17] I. Vaisman, Lagrange geometry on tangent manifolds, Int. J. Math. Math. Sci. 51, 3241-3266, 2003.