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Mat. Zametki, 2004, Volume 76, Issue 6, Pages 868–873 (Mi mz158)  

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

Nil-Manifolds Cannot be Immersed as Hypersurfaces in Euclidean Spaces

L. A. Masal'tsev

V. N. Karazin Kharkiv National University

Abstract: We prove that the $2n+1$-dimensional Heisenberg group $H_n$ and the $4$-manifolds $\operatorname{Nil}^4$ and $\operatorname{Nil}^3\times\mathbb R$ endowed with an arbitrary left-invariant metric admit no $C^3$-regular immersions into Euclidean spaces $\mathbb R^{2n+2}$ and $\mathbb R^5$, respectively.

DOI: https://doi.org/10.4213/mzm158

Full text: PDF file (191 kB)
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English version:
Mathematical Notes, 2004, 76:6, 810–815

Bibliographic databases:

UDC: 514
Received: 25.09.2003
Revised: 30.03.2004

Citation: L. A. Masal'tsev, “Nil-Manifolds Cannot be Immersed as Hypersurfaces in Euclidean Spaces”, Mat. Zametki, 76:6 (2004), 868–873; Math. Notes, 76:6 (2004), 810–815

Citation in format AMSBIB
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\by L.~A.~Masal'tsev
\paper Nil-Manifolds Cannot be Immersed as Hypersurfaces in Euclidean Spaces
\jour Mat. Zametki
\yr 2004
\vol 76
\issue 6
\pages 868--873
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\transl
\jour Math. Notes
\yr 2004
\vol 76
\issue 6
\pages 810--815
\crossref{https://doi.org/10.1023/B:MATN.0000049680.35564.6f}
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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. A. A. Borisenko, “On Isometric Immersion of Nilmanifolds in Euclidean space”, Math. Notes, 87:1 (2010), 122–124  mathnet  crossref  crossref  mathscinet  zmath  isi
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