Traceless cubic forms on statistical manifolds and Tchebychev geometry
Volume 69 / 2005
Banach Center Publications 69 (2005), 179-187
MSC: Primary 53A15; Secondary 53A30, 53B05, 53B25.
DOI: 10.4064/bc69-0-13
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.
