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 Ufimsk. Mat. Zh., 2018, Volume 10, Issue 2, Pages 43–56 (Mi ufa431)

Influence of stratification on the groups of conformal transformations of pseudo-Riemannian orbifolds

N. I. Zhukova

National Research University Higher School of Economics, Bol'shaya Pecherskaya str. 25/12, 603155, Nizhny Novgorod, Russia

Abstract: 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 pseudo-Riemannian orbifolds. We show that a conformal pseudo-Riemannian geometry is induced on each stratum of such orbifold. Due to this, for $k\in\{0,1\}\cup\{3,\ldots,n-1\}$, we obtain exact estimates for the dimensions of the conformal transformation groups of $n$-dimensional pseudo-Riemannian orbifolds admitting $k$-dimensional stratum with essential groups of conformal transforms. A key fact in obtaining these estimates is that each connected transformation group of an orbifold preserves every connected component of each its stratum.
The influence of stratification of $n$-dimensional pseudo-Riemann orbifold 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 complete 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.

Keywords: orbifold, conformal pseudo-Riemannian geometry, conformal transformation, Lie group.

 Funding Agency Grant Number National Research University Higher School of Economics 16-01-0010 Ministry of Education and Science of the Russian Federation The manuscript is prepared in the framework of Program “Scientific foundation of National Research University Higher School of Economics” (project no. 16-01-0010) and in the framework of state support for leading universities of Russian Federation “5-100”.

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English version:
Ufa Mathematical Journal, 2018, 10:2, 44–57 (PDF, 416 kB); https://doi.org/10.13108/2018-10-2-44

Bibliographic databases:

UDC: 514.7
MSC: 53C50, 53A30

Citation: N. I. Zhukova, “Influence of stratification on the groups of conformal transformations of pseudo-Riemannian orbifolds”, Ufimsk. Mat. Zh., 10:2 (2018), 43–56; Ufa Math. J., 10:2 (2018), 44–57

Citation in format AMSBIB
\Bibitem{Zhu18} \by N.~I.~Zhukova \paper Influence of stratification on the groups of conformal transformations of pseudo-Riemannian orbifolds \jour Ufimsk. Mat. Zh. \yr 2018 \vol 10 \issue 2 \pages 43--56 \mathnet{http://mi.mathnet.ru/ufa431} \transl \jour Ufa Math. J. \yr 2018 \vol 10 \issue 2 \pages 44--57 \crossref{https://doi.org/10.13108/2018-10-2-44} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438890500004} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048493465}