Masal’tsev, L. A. Nil-manifolds cannot be immersed as hypersurfaces in Euclidean spaces. (English. Russian original) Zbl 1114.53051 Math. Notes 76, No. 6, 810-815 (2004); translation from Mat. Zametki 76, No. 6, 868-873 (2004). Summary: We prove that the \(2n + 1\)-dimensional Heisenberg group \(H_n\) and the 4-manifolds \(\text{Nil}^4\) and \(\text{Nil}^3 \times \mathbb R\) 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. Cited in 2 Documents MSC: 53C40 Global submanifolds 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) Keywords:nil-manifold; Heisenberg group; left-invariant metric; immersion; Smale-Hirsch theorem PDFBibTeX XMLCite \textit{L. A. Masal'tsev}, Math. Notes 76, No. 6, 810--815 (2004; Zbl 1114.53051); translation from Mat. Zametki 76, No. 6, 868--873 (2004) Full Text: DOI