Comptes Rendus
no. 11-12
Differential Geometry
On extrinsic symmetric spaces with zero mean curvature in Minkowski space-time
[Sur les espaces symétriques extrinsèques à courbure moyenne nulle dans lʼespace-temps de Minkowski]

Présenté par : the Editorial Board

Jong Ryul Kim1
1 Department of Mathematics, Kunsan National University, Kunsan, 573-701, Republic of Korea
Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 471-475.

Pour un espace symétrique extrinsèque M dans lʼespace-temps de Minkowski, nous prouvons que, si M est de type espace et à courbure moyenne nulle, alors M est totalement géodésique, tandis que, si M est de type temps à courbure moyenne nulle, il sʼagit alors dʼune sous-variété totalement géodésique ou dʼune hypersurface.

For an extrinsic symmetric space M in Minkowski space-time, we prove that if M is spacelike with zero mean curvature, then it is totally geodesic and if M is timelike with zero mean curvature, then it is totally geodesic or it is a flat hypersurface.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.06.005
Jong Ryul Kim 1

1 Department of Mathematics, Kunsan National University, Kunsan, 573-701, Republic of Korea 
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Jong Ryul Kim. On extrinsic symmetric spaces with zero mean curvature in Minkowski space-time. Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 471-475. doi : 10.1016/j.crma.2013.06.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.06.005/

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[3] D. Ferus Produkt-Zerlegung von Immersionen mit paralleler zweiter Fundamentalform, Math. Ann., Volume 211 (1974), pp. 1-5

[4] D. Ferus Immersions with parallel second fundamental form, J. Differential Geom., Volume 5 (1974), pp. 333-340

[5] D. Ferus Symmetric submanifolds of Euclidean space, Math. Ann., Volume 247 (1980), pp. 81-93

[6] J.R. Kim; J.-H. Eschenburg Indefinite extrinsic symmetric spaces, Manuscr. Math., Volume 135 (2011), pp. 203-214

[7] T. Neukirchner Solvable pseudo-Riemannian symmetric spaces | arXiv

[8] W. Strübing Symmetric submanifolds of Riemannian manifolds, Math. Ann., Volume 245 (1979), pp. 37-44

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