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VECTORIAL LINEAR CONNECTIONS

  • Hwajeong Kim (Department of Mathematics Hannam National University)
  • 투고 : 2023.04.06
  • 심사 : 2023.08.07
  • 발행 : 2023.08.31

초록

In this article, we consider a vectorial linear connection which is determined by three fixed vector fields. Classifying these vectorial connections, we obtain a new type of generalized statistical manifolds which allow non-zero torsion.

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참고문헌

  1. I. Agricola, The srni lectures on non-integrable geometries with torsion, Proceedings of the 26th Winter School, Geometry and Physics 2006.
  2. S. Amari, Information Geometry and Its Applications, Applied Mathematical Sciences. Springer Japan (2016).
  3. A.M.Blaga, A. Nannicini, Conformal-projective transformations on statistical and semi-Weyl manifolds with torsion arXiv.2209.00689vl, (2022)
  4. O.Calin, C. Udriste, Geometric Modeling in Probability and Statistics, Springer (2013)
  5. E. Cartan, Sur les varietes a connexion affine et la theorie de la relativite generalisee, Ann. Ec. Norm. Sup. 42 (1925), 17-88, English transl. by Magnon and A. Ashtekar, On manifolds with an affine conneciton and the theory of general relativity, Napoli: Bibliopolis (1986). https://doi.org/10.24033/asens.761
  6. G.B.Folland, Weyl Manifolds, J. Diff. Geometry 4 (1970), 145-153.
  7. H. Kim, A note on statistical manifolds with torsion, Communi. Korean Math. Soc., 38 (2023), No. 2, 621-628.
  8. T. Kurose, Statistical manifolds admitting torsion. Geometry and Something. (2007), in Japanese.
  9. H. Matsuzoe Statistical manifolds and affine differential geometry, Advanced Studies in Pure Mathematics 57, Probabilistic Approach to Geometry (2010), 303-321.
  10. A. P. Norden, On pairs of conjugate parallel displacements in multidimensional spaces, In Doklady Akademii nauk SSSR, 49 (1945), 1345-1347.
  11. H. Nagaoka, S. Amari, Differential geometry of smooth families of probability distributions, Technical Report (METR) 82-7, Dept. of Math. Eng. and Instr. Phys. Univ. of Tokyo, (1982)
  12. F. Tricerri, L. Vanhecke, Homogeneous structures on Riemannian manifolds, London Math. Soc., Lecture Notes Series, 83 (1983)