Geometry of semi-Weyl manifolds and Weyl manifolds (Q2731412)

The paper introduces a new class of pseudo-Riemannian manifolds. The author calls it semi-Weyl manifolds. This new class is regarded as a natural generalization of Weyl manifold [cf. \textit{D. M. J. Calderbank} and \textit{H. Pedersen}, Einstein-Weyl geometry, Surv. Differ. Geom., Suppl. J. Differ. Geom. 6, 387-423 (1999; Zbl 0996.53030)] and a class of statistical manifolds [cf. \textit{S. L. Lauritzen}, Statistical manifolds, Differential geometry in statistical inference, IMS Lecture Notes Monograph Series, 10, Hayward, California, pp. 96-163 (1987; Zbl 0694.62001)]. Moreover some applications are given. In particular, it is shown that every Weyl manifold induced by an affine hypersurface immersion is a locally trivial Einstein-Weyl manifold.