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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc69-0-13,
author = {Hiroshi Matsuzoe},
title = {Traceless cubic forms on statistical manifolds and Tchebychev geometry},
journal = {Banach Center Publications},
volume = {68},
year = {2005},
pages = {179-187},
zbl = {1099.53008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc69-0-13}
}
Hiroshi Matsuzoe. Traceless cubic forms on statistical manifolds and Tchebychev geometry. Banach Center Publications, Tome 68 (2005) pp. 179-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc69-0-13/