Traceless cubic forms on statistical manifolds and Tchebychev geometry

Tom 69 / 2005

Hiroshi Matsuzoe Banach Center Publications 69 (2005), 179-187 MSC: Primary 53A15; Secondary 53A30, 53B05, 53B25. DOI: 10.4064/bc69-0-13

Streszczenie

Geometry of traceless cubic forms is studied. It is shown that the traceless part of the cubic form on a statistical manifold determines a conformal-projective equivalence class of statistical manifolds. This conformal-projective equivalence on statistical manifolds is a natural generalization of conformal equivalence on Riemannian manifolds. As an application, Tchebychev type immersions in centroaffine immersions of codimension two are studied.

Autorzy

  • Hiroshi MatsuzoeDepartment of Computer Science and Engineering
    Graduate School of Engineering
    Nagoya Institute of Technology
    Gokiso-cho, Showa-ku
    Nagoya, 466-8555, Japan
    e-mail

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