|
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
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
Citation:
N. R. Kamyshanskii, “The classification of pseudo-Riemannian spaces $V^n$ with poles for $n\geqslant3$”, Mat. Sb. (N.S.), 105(147):1 (1978), 28–62; Math. USSR-Sb., 34:1 (1978), 25–54
Linking options:
https://www.mathnet.ru/eng/sm2515https://doi.org/10.1070/SM1978v034n01ABEH001040 https://www.mathnet.ru/eng/sm/v147/i1/p28
|
Statistics & downloads: |
Abstract page: | 198 | Russian version PDF: | 70 | English version PDF: | 3 | References: | 23 |
|