Geodesic
Nil-Manifolds Cannot be Immersed as Hypersurfaces in Euclidean Spaces
Matematičeskie zametki, Tome 76 (2004) no. 6, pp. 868-873 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{MZM_2004_76_6_a6,
     author = {L. A. Masal'tsev},
     title = {Nil-Manifolds {Cannot} be {Immersed} as {Hypersurfaces} in {Euclidean} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {868--873},
     year = {2004},
     volume = {76},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_6_a6/}
}
TY  - JOUR
AU  - L. A. Masal'tsev
TI  - Nil-Manifolds Cannot be Immersed as Hypersurfaces in Euclidean Spaces
JO  - Matematičeskie zametki
PY  - 2004
SP  - 868
EP  - 873
VL  - 76
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_2004_76_6_a6/
LA  - ru
ID  - MZM_2004_76_6_a6
ER  - 
%0 Journal Article
%A L. A. Masal'tsev
%T Nil-Manifolds Cannot be Immersed as Hypersurfaces in Euclidean Spaces
%J Matematičeskie zametki
%D 2004
%P 868-873
%V 76
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_2004_76_6_a6/
%G ru
%F MZM_2004_76_6_a6
L. A. Masal'tsev. Nil-Manifolds Cannot be Immersed as Hypersurfaces in Euclidean Spaces. Matematičeskie zametki, Tome 76 (2004) no. 6, pp. 868-873. http://geodesic.mathdoc.fr/item/MZM_2004_76_6_a6/

[1] Rivertz H. J., An obstruction to isometric immersion of the threedimensional Heisenberg group into $\mathbb R^4$, Preprint series in Pure Mathematics No. 22, Matematick institut Univ. Oslo, Oslo, 1999

[2] Gromov M., Differentsialnye sootnosheniya s chastnymi proizvodnymi, Mir, M., 1990

[3] Hillman J. A., Four-manifolds, Geometries and Knots, Geometry and Topology Monographs, 5, University of Sydney, 2002 | MR

[4] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, T. 2, Nauka, M., 1981

[5] Gordon C., “Riemannian manifolds isospectral on functions but not on $1$-forms”, J. Differential Geometry, 24 (1986), 79–96 | MR | Zbl

[6] Besse A., Mnogoobraziya Einshteina, Mir, M., 1990 | Zbl

[7] Aminov Yu. A., Geometriya podmnogoobrazii, Naukova dumka, Kiev, 2002 | Zbl