Ufa Mathematical Journal
    Volume 10, Number 2, pp. 44-57

    The influence of stratification on the groups of conformal transformations of pseudo-Riemannian orbifolds

    Zhukova N.I.


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    We study the groups of conformal transformations of $n$-dimensional pseudo-Riemannian orbifolds $({\mathcal N},g)$ as $n\geq 3$. We extend the Alekseevskii method for studying conformal transformation groups of Riemannian manifolds to psevdo-Riemannian orbifolds. We show that a conformal pseudo-Riemannian geometry is induced on each stratum of that orbifold. Due to this, for $k\in\{0,1\}\cup\{3,\ldots,n-1\}$, we obtain exact estimates for the 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. A key fact in obtaining these estimates is that each connected transformation group of an orbifold preserves every connected component of each its strata. The influence of stratification of $n$-dimensional pseudo-Riemann orbi\-fold to the similarity transformation group of this orbifold is also studied for $n\geq 2$. We prove that the obtained estimates for the dimension of the comp\-lete essential groups of conformal transformations and the similarity transformation groups of $n$-dimensional pseudo-Riemann orbifolds are sharp; this is done by adducing corresponding examples of locally flat pseudo-Riemannian orbifolds