Tohoku Mathematical Journal

On the divergences of $1$-conformally flat statistical manifolds

Takashi Kurose

Full-text: Open access

Article information

Tohoku Math. J. (2), Volume 46, Number 3 (1994), 427-433.

First available in Project Euclid: 3 May 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C05: Connections, general theory
Secondary: 53A15: Affine differential geometry


Kurose, Takashi. On the divergences of $1$-conformally flat statistical manifolds. Tohoku Math. J. (2) 46 (1994), no. 3, 427--433. doi:10.2748/tmj/1178225722.

Export citation


  • [Al] S. -I. AMARI, Differential Geometrical Methods in Statistics, Lecture Notes in Statist. 28, Springer-Verlag, New York, 1985.
  • [A2] S. -I. AMARI, Differential geometrical theory of statistics, Differential Geometry in Statistica Inference, IMS Lecture Notes-Monograph Series, vol. 10, Inst. Math. Statist., Hayward, California, 1987.
  • [BNJK] O. E. BARNDORFF-NIELSEN, P. E. JUPP AND W. S. KENDALL, Stochastic calculus, statistica asymptotics, Taylor strings and phyla, Dept. of Theoretical Statistics, Institute of Mathematics, Univ. of Aarhus, Research Reports 236, 1991.
  • [DNV] F. DILLEN, K. NOMIZU AND L. VRANCKEN, Conjugate connections and Radon's theorem in affin differential geometry, Monatsh. Math. 109 (1990), 221-235.
  • [E] S. EGUCHI, Geometry of minimum contrast, Hiroshima Math. J. 22 (1992), 631-647
  • [Kl] T. KUROSE, Dual connections and affine geometry, Math. Z. 203 (1990), 115-121
  • [K2] T. KUROSE, On the Minkowski problem in affine geometry, Results Math. 20 (1991), 643-649
  • [K3] T. KUROSE, Dual connections and projective geometry, Hiroshima Math. J. 23 (1993), 327-332
  • [M] T. MATUMOTO, Any statistical manifold has a contrast function--On the C3-functions taking th minimum at the diagonal of the product manifold--, preprint.
  • [N] K. NOMIZU, Introduction to affine differential geometry, Part I, MPI preprint MPI 88-37, 1988
  • [NO] K. NOMIZU AND B. OPOZDA, On normal and conormal maps for affine hypersurfaces, Thok Math. J. 44 (1992), 425-431.
  • [NP] K. NOMIZU AND U. PINKALL, On the geometry of affine immersions, Math. Z. 195(1987), 165-178
  • [NS] K. NOMIZU AND U. SIMON, Notes on conjugate connections, in Geometry and Topology o Submanifolds, IV (F. Dillen and L. Verstraelen, eds.), World Scientific, 1992, pp. 152-173.
  • [OAT] I. OKAMOTO, S. -I. AMARI AND K. TAKEUCHI, Asymptotic theory of sequential estimation: differentia geometrical approach, Ann. Statist. 19 (1991), 961-981.