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Mathematics of the USSR-Sbornik, 1978, Volume 34, Issue 1, Pages 25–54
DOI: https://doi.org/10.1070/SM1978v034n01ABEH001040
(Mi sm2515)
 

This article is cited in 1 scientific paper (total in 1 paper)

The classification of pseudo-Riemannian spaces $V^n$ with poles for $n\geqslant3$

N. R. Kamyshanskii
References:
Abstract: The goal of this article is the description of all complete, simply-connected, analytic pseudo-Riemannian spaces $V^n$ of dimension $n\geqslant3$ and index $k$ which contain at least one pole. Recall that a point $p$ in $V^n$ is called a pole if the group of motions of $V^n$ which fix $p$ has dimension $n(n-1)/2$. To each complete space $V^n$ ($n\geqslant3$) with poles there corresponds a class $\chi(V^n)$ of real analytic functions on $\mathbf R$, the characteristic functions for the space $V^n$; the group of affine transformations of the line $\mathbf R$ acts transitively on $\chi(V^n)$. A necessary and sufficient condition is stated for a given real analytic function $a(\tau)$ on $\mathbf R$ to be a characteristic function for an analytic pseudo-Riemannian space $V^n$ ($n\geqslant3$) which contains a pole. A simply-connected space $V^n$ of index $k$ is uniquely determined (up to isometry) by its characteristic function. In the article is an example of a complete, simply-connected, analytic pseudo-Riemannian space $\widetilde V^n_0$ of dimension $n\geqslant3$ and index $k$ for which the set of poles is infinite. It is shown that every complete, simply-connected, analytic pseudo-Riemannian space of dimension $n\geqslant3$ and index $k$ which has poles is conformally equivalent to a region in $\widetilde V^n_0$.
Figures: 2.
Bibliography: 3 titles.
Received: 09.12.1976
Bibliographic databases:
UDC: 513.78
MSC: Primary 53C50; Secondary 53B30
Language: English
Original paper language: Russian
Citation: N. R. Kamyshanskii, “The classification of pseudo-Riemannian spaces $V^n$ with poles for $n\geqslant3$”, Math. USSR-Sb., 34:1 (1978), 25–54
Citation in format AMSBIB
\Bibitem{Kam78}
\by N.~R.~Kamyshanskii
\paper The classification of pseudo-Riemannian spaces $V^n$ with poles for~$n\geqslant3$
\jour Math. USSR-Sb.
\yr 1978
\vol 34
\issue 1
\pages 25--54
\mathnet{http://mi.mathnet.ru//eng/sm2515}
\crossref{https://doi.org/10.1070/SM1978v034n01ABEH001040}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=474156}
\zmath{https://zbmath.org/?q=an:0372.53024|0406.53040}
Linking options:
  • https://www.mathnet.ru/eng/sm2515
  • https://doi.org/10.1070/SM1978v034n01ABEH001040
  • https://www.mathnet.ru/eng/sm/v147/i1/p28
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:218
    Russian version PDF:72
    English version PDF:11
    References:29
     
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