### Book chapter

## Характеристика Эйлера-Сатаки компактных аффинных орбифолдов

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.