Влияние стратификации на группы конформных преобразований псевдоримановых орбифолдов

Уфимский математический журнал. 2018. Т. 10. № 2. С. 43–56.

Zhukova N.

The groups of conformal transformations of $n$-dimensional
pseudo-Riemannian orbifolds $({\mathcal N},g)$ are investigated for $n\geq 3$.
The Alekseevskii method of the investigation of the conformal transformation groups of
Riemannian manifolds is extended by us to psevdo-Riemannian orbifolds. It is shown that
a conformal pseudo-Riemannian geometry is induced on each stratum of that orbifold. Due to this,
for $k\in\{0,1\}\cup\{3,...,n-1\}$ exact estimates of dimensions of the conformal
transformati\-on groups of $n$-dimensional pseudo-Rieman\-ni\-an orbifolds admitting $k$-dimen\-si\-onal
strata with essential conformal trans\-for\-ma\-tion groups are obtained.
A key fact in obtaining these estimates is that any connected transformation group of an
orbifold preserves every connected component of any of its strata.

The influence of stratification of $n$-dimensional pseudo-Riemann orbi\-fold
to the similarity transformation group of this orbifold is also investi\-ga\-ted for $n\geq 2$.

The exactness of the obtained estimates of the dimension of comp\-lete essential groups of conformal
transformations and the similarity transformation groups of $n$-dimensional pseudo-Riemann orbifolds
are pro\-ved by constructing the constructing examples of locally flat pseudo-Rieman\=nian orbifolds

Keywords: Группа Ли, орбифолд, Lie group, orbifold, conformal transformation, conformal pseudo-Riemannian geometry, конформная псевдориманова геометрия, конформное преобразование

Publication based on the results of: Жесткие геометрии и группы их автоморфизмов на сингулярных пространствах слоев слоений со связностями Эресмана (2016)