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Mat. Sb., 2006, Volume 197, Number 2, Pages 3–16 (Mi msb1507)  

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

Families of submanifolds of constant negative curvature of many-dimensional Euclidean space

Yu. A. Aminov

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine

Abstract: A family of $n$-dimensional submanifolds of constant negative curvature $K_0$ of the $(2n-1)$-dimensional Euclidean space $E^{2n-1}$ is considered and included in an orthogonal system of coordinates. For $n=2$ such a system of coordinates was considered by Bianchi. The concept of a many-dimensional Bianchi system of coordinates is introduced. The following result is central in the paper.
Theorem 1. {\it Assume that a ball of radius $\rho$ in the Euclidean space $E^{2n-1}$ carries a regular Bianchi system of coordinates such that $K_0\leqslant -1$. Then}
$$ \rho\leqslant\frac\pi4 . $$

Bibliography: 12 titles.

DOI: https://doi.org/10.4213/sm1507

Full text: PDF file (442 kB)
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English version:
Sbornik: Mathematics, 2006, 197:2, 139–152

Bibliographic databases:

UDC: 514
MSC: Primary 53A05, 53B25; Secondary 53C21
Received: 11.01.2005

Citation: Yu. A. Aminov, “Families of submanifolds of constant negative curvature of many-dimensional Euclidean space”, Mat. Sb., 197:2 (2006), 3–16; Sb. Math., 197:2 (2006), 139–152

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. G. Szajewska, “A Property of the Curvature and Torsion of a Regular Family of Curves in $E^n$”, Math. Notes, 83:5 (2008), 688–692  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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