Международная конференция «Современная геометрия и её приложения - 2019»: сборник трудов
According to Chern's conjecture, the Euler characteristic of a closed affine manifold must be zero. We prove the equivalence of this Chern conjecture to the following conjecture for orbifolds: the Euler--Sataki characteristic of a compact affine orbifold is zero. We found the conditions under which the Euler--Sataki characteristic of a compact affine orbifold vanishes. Examples are constructed.
The relations between the geometric properties of fibered pseudo-Riemannian manifolds and their bases are investigated. Special attention is paid to Lorentzian manifolds and causality conditions. Keywords: principal bundle, G-connection, lorentzian manifold, space-time, causality condition