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Izv. Akad. Nauk SSSR Ser. Mat., 1975, Volume 39, Issue 5, Pages 1093–1129 (Mi izv2081)  

This article is cited in 3 scientific papers (total in 3 papers)

Poles of pseudo-Riemannian spaces

A. S. Solodovnikov, N. R. Kamyshanskii


Abstract: Two-dimensional complete analytic pseudo-Riemannian spaces $V$ with poles are studied. A pole is a point $p\in V$ with respect to which $V$ admits a one-parameter group of rotations. With each pole is connected a holomorphic function $F_p(z)$ (the complex pole function). Necessary conditions on $F_p(z)$ are established. A number of “existence theorems” are proved: for a given holomorphic function $F(z)$ with certain properties there exists a complete space $V$ with pole $p$ for which the function $F_p(z)$ coincides with $F(z)$.

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English version:
Mathematics of the USSR-Izvestiya, 1975, 9:5, 1035–1068

Bibliographic databases:

UDC: 513.78
MSC: 53C20
Received: 01.07.1974

Citation: A. S. Solodovnikov, N. R. Kamyshanskii, “Poles of pseudo-Riemannian spaces”, Izv. Akad. Nauk SSSR Ser. Mat., 39:5 (1975), 1093–1129; Math. USSR-Izv., 9:5 (1975), 1035–1068

Citation in format AMSBIB
\Bibitem{SolKam75}
\by A.~S.~Solodovnikov, N.~R.~Kamyshanskii
\paper Poles of pseudo-Riemannian spaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1975
\vol 39
\issue 5
\pages 1093--1129
\mathnet{http://mi.mathnet.ru/izv2081}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=402656}
\zmath{https://zbmath.org/?q=an:0319.53021}
\transl
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 5
\pages 1035--1068
\crossref{https://doi.org/10.1070/IM1975v009n05ABEH001507}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. R. Kamyshanskii, “The classification of pseudo-Riemannian spaces $V^n$ with poles for $n\geqslant3$”, Math. USSR-Sb., 34:1 (1978), 25–54  mathnet  crossref  mathscinet  zmath
    2. N. R. Kamyshanskii, A. S. Solodovnikov, “Semireducible analytic spaces “in the large””, Russian Math. Surveys, 35:5 (1980), 1–56  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Igoshin V.A., “Kletochnaya struktura psevdorimanova prostranstva s geodezicheskim polem odnomernykh napravlenii”, Trudy NGTU im. R.E. Alekseeva, 2012, no. 1, 349–359  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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