Three-dimensional curvature homogeneous hypersurfaces
Calvaruso, Giovanni ; Marinosci, Rosa Anna ; Perrone, Domenico
Archivum Mathematicum, Tome 036 (2000), p. 269-278 / Harvested from Czech Digital Mathematics Library

This paper is motivated by the open problem whether a three-dimensional curvature homogeneous hypersurface of a real space form is locally homogeneous or not. We give some partial positive answers.

Publié le : 2000-01-01
Classification:  53C20,  53C30,  53C40
@article{107741,
     author = {Giovanni Calvaruso and Rosa Anna Marinosci and Domenico Perrone},
     title = {Three-dimensional curvature homogeneous hypersurfaces},
     journal = {Archivum Mathematicum},
     volume = {036},
     year = {2000},
     pages = {269-278},
     zbl = {1054.53070},
     mrnumber = {1811171},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107741}
}
Calvaruso, Giovanni; Marinosci, Rosa Anna; Perrone, Domenico. Three-dimensional curvature homogeneous hypersurfaces. Archivum Mathematicum, Tome 036 (2000) pp. 269-278. http://gdmltest.u-ga.fr/item/107741/

Boeckx E.; Kowalski O.; Vanhecke L., Riemannian manifolds of conullity two, World Scientific 1996. (1996) | MR 1462887 | Zbl 0904.53006

Calvaruso G.; Vanhecke L. Special ball-homogeneous spaces, Z. Anal. Anwendungen (4) 16 (1997), 789-800. (1997) | MR 1615680 | Zbl 0892.53023

Calvaruso G.; Vanhecke L. Ball-homogeneous spaces, Proceedings of the Workshop on Differential Geometry, Santiago 89 (1998), 35-51. (1998) | Zbl 0912.53034

Cartan E. Sur des familles remarquables d’hypersurfaces isoparamétriques dans les espaces sphériques, Math. Z. 45 (1939), 335-367. (1939) | MR 0000169 | Zbl 0021.15603

Cecil T. E.; Ryan P. J. Tight and taut immersions of manifolds, Research Notes in Math., Pitman 1985. (1985) | MR 0781126 | Zbl 0596.53002

Chang S. A closed hypersurface with constant scalar and mean curvature in $S^4$ is isoparametric, Comm. Anal. Geom. (1) 1 (1993), 71-100. (1993) | MR 1230274

Ferus D. Notes on isoparametric hypersurfaces, Escola de Geometria Diferencial, Universidade Estadual de Campinas, 1980. (1980)

Ferus D.; Karcher H.; Münzner H. F. Clifford algebren und neue isoparametrische hyperflächen, Math. Z. (1981), 479-502. (1981)

Kowalski O. A classification of Riemannian $3$-manifolds with constant principal Ricci curvatures $\varrho _1 =\varrho _2 \ne \varrho _3$, Nagoya Math. J. 132 (1993), 1-36. (1993) | MR 1253692

Ozeki H.; Takeuchi M. On some types of isoparametric hypersurfaces in spheres, I, Tôhoku Math. J. 27 (1975), 515-559. (1975) | MR 0454888 | Zbl 0359.53011

Ozeki H.; Takeuchi M. On some types of isoparametric hypersurfaces in spheres, I, Tôhoku Math. J. 28 (1976), 7-55. (1976) | MR 0454889

Sekigawa K. On some $3$-dimensional Riemannian manifolds, Hokkaido Math. J. 26 (1974), 259-270. (1974) | MR 0353204

Singer I. M. Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685-697. (1960) | MR 0131248 | Zbl 0171.42503

Takagi H. On curvature homogeneity of Riemannian manifolds, Tôhoku Math. J. 26 (1974), 581-585. (1974) | MR 0365417 | Zbl 0302.53022

Tricerri F.; Vanhecke L. Cartan hypersurfaces and reflections, Nihonkai Math. J. (2) 1 (1990), 203-208. (1990) | MR 1090781 | Zbl 0956.53505

Tsukada K. Curvature homogeneous hypersurfaces immersed in a real space form, Tôhoku Math. J. 40 (1988), 221-244. (1988) | MR 0943821 | Zbl 0651.53037

Yamada A. Homogeneity of hypersurfaces in a sphere, Tsukuba J. Math. 22 (1) (1998), 131-143. (1998) | MR 1637672 | Zbl 0981.53040

Yamato K. A characterization of locally homogeneous Riemann manifolds of dimension $3$, Nagoya Math. J. 123 (1991), 77-90. (1991) | MR 1126183 | Zbl 0738.53032