References
[B] Bernoulli, J.: Opera. Tomus Secundus, Culture et Civilisation, Brussels (1967)
[D] Deprez, J.: Semi-parallel hypersurfaces. Rend. Semin. Mat. Univ. Politec. Torino44, 303–316 (1986)
[F] Ferus, D.: Symmetric submanifolds of Euclidean space. Math. Ann.247, 81–93 (1980)
[H-N] Hartman, P., Nirenberg, L.: On spherical image maps whose Jacobians do not change sign. Am. J Math.81, 901–920 (1959)
[L]1 Lumiste, Ü.: Submanifolds with a Van der Waerden-Bortolotti plane connection and parallelism of the third fundamental form. Izv. Vyssh. Uchebn. Zaved., Mat.31, 18–27 (1987)
[L]2 Lumiste, Ü.: Classification of two-codimensional semi-symmetric submanifolds. Tartu Riikl. Ül. Toimetised37, 79–93 (1988)
[N] Nomizu, K.: On hypersurfaces satisfying a certain condition on the curvature tensor, Tôhoku Math. J.20, 46–59 (1968)
[N-O] Nomizu, K., Ozeki, H.: A theorem on curvature tensor fields. Proc. Natl. Acad. Sci. USA48, 206–207 (1962)
[R] Ryan, P.J.: Homogeneity and some curvature conditions for hypersurfaces. Tôhoku Math. J.21, 363–388 (1969)
[S-W] Simon, U., Weinstein, A.: Anwendungen der de Rham Zerlegung auf Probleme der lokalen Flächentheorie. Manuscr. Math.1, 139–146 (1969)
[S] Strübing, W.: Symmetric submanifolds of Riemannian manifolds. Math. Ann.245, 37–44 (1979)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dillen, F. The classification of hypersurfaces of a Euclidean space with parallel higher order fundamental form. Math Z 203, 635–643 (1990). https://doi.org/10.1007/BF02570761
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02570761