Kim, Jong Ryul On extrinsic symmetric spaces with zero mean curvature in Minkowski space-time. (English. French summary) Zbl 1275.53023 C. R., Math., Acad. Sci. Paris 351, No. 11-12, 471-475 (2013). Summary: For an extrinsic symmetric space \(M\) in Minkowski space-time, we prove that if \(M\) is space-like with zero mean curvature, then it is totally geodesic and if \(M\) is time-like with zero mean curvature, then it is totally geodesic or it is a flat hypersurface. MSC: 53B25 Local submanifolds 53B30 Local differential geometry of Lorentz metrics, indefinite metrics Keywords:Minkowski space-time; zero mean curvature; totally geodesic; flat hypersurface PDFBibTeX XMLCite \textit{J. R. Kim}, C. R., Math., Acad. Sci. Paris 351, No. 11--12, 471--475 (2013; Zbl 1275.53023) Full Text: DOI Link References: [1] Cahen, M.; Parker, M., Pseudo-Riemannian symmetric spaces, Mem. Amer. Math. Soc., 229, 1-108 (1980) · Zbl 0438.53057 [2] Eschenburg, J.-H.; Heintze, E., Extrinsic symmetric spaces and orbits of s-representations, Manuscr. Math., 88, 517-524 (1995) · Zbl 0857.53033 [3] Ferus, D., Produkt-Zerlegung von Immersionen mit paralleler zweiter Fundamentalform, Math. Ann., 211, 1-5 (1974) · Zbl 0273.53044 [4] Ferus, D., Immersions with parallel second fundamental form, J. Differential Geom., 5, 333-340 (1974) [5] Ferus, D., Symmetric submanifolds of Euclidean space, Math. Ann., 247, 81-93 (1980) · Zbl 0446.53041 [6] Kim, J. R.; Eschenburg, J.-H., Indefinite extrinsic symmetric spaces, Manuscr. Math., 135, 203-214 (2011) · Zbl 1219.53053 [7] Neukirchner, T., Solvable pseudo-Riemannian symmetric spaces [8] Strübing, W., Symmetric submanifolds of Riemannian manifolds, Math. Ann., 245, 37-44 (1979) · Zbl 0424.53025 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.