Traceless cubic forms on statistical manifolds and Tchebychev geometry

Hiroshi Matsuzoe. "Traceless cubic forms on statistical manifolds and Tchebychev geometry." Banach Center Publications 69.1 (2005): 179-187. <http://eudml.org/doc/282473>.

@article{HiroshiMatsuzoe2005,
abstract = {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.},
author = {Hiroshi Matsuzoe},
journal = {Banach Center Publications},
keywords = {traceless cubic form; conformal-projective geometry; Chebyshev geometry; centroaffine immersion of codimension two; statistical manifold},
language = {eng},
number = {1},
pages = {179-187},
title = {Traceless cubic forms on statistical manifolds and Tchebychev geometry},
url = {http://eudml.org/doc/282473},
volume = {69},
year = {2005},
}

TY - JOUR
AU - Hiroshi Matsuzoe
TI - Traceless cubic forms on statistical manifolds and Tchebychev geometry
JO - Banach Center Publications
PY - 2005
VL - 69
IS - 1
SP - 179
EP - 187
AB - 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.
LA - eng
KW - traceless cubic form; conformal-projective geometry; Chebyshev geometry; centroaffine immersion of codimension two; statistical manifold
UR - http://eudml.org/doc/282473
ER -