This article is cited in 4 papers

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.

UDC: 514

Received: 25.09.2003
Revised: 30.03.2004

DOI: 10.4213/mzm158

 English version: Mathematical Notes, 2004, 76:6, 810–815

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