Keywords: curvature homogeneous spaces; isoparametric hypersurfaces
@article{ARM_2000_36_4_a3,
author = {Calvaruso, G. and Marinosci, R. A. and Perrone, D.},
title = {Three-dimensional curvature homogeneous hypersurfaces},
journal = {Archivum mathematicum},
pages = {269--278},
year = {2000},
volume = {36},
number = {4},
mrnumber = {1811171},
zbl = {1054.53070},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ARM_2000_36_4_a3/}
}
Calvaruso, G.; Marinosci, R. A.; Perrone, D. Three-dimensional curvature homogeneous hypersurfaces. Archivum mathematicum, Tome 36 (2000) no. 4, pp. 269-278. http://geodesic.mathdoc.fr/item/ARM_2000_36_4_a3/
[1] Boeckx E., Kowalski O., Vanhecke L.,: Riemannian manifolds of conullity two. World Scientific 1996. | MR | Zbl
[2] Calvaruso G., Vanhecke L.: Special ball-homogeneous spaces. Z. Anal. Anwendungen (4) 16 (1997), 789-800. | MR | Zbl
[3] Calvaruso G., Vanhecke L.: Ball-homogeneous spaces. Proceedings of the Workshop on Differential Geometry, Santiago 89 (1998), 35-51. | Zbl
[4] Cartan E.: Sur des familles remarquables d’hypersurfaces isoparamétriques dans les espaces sphériques. Math. Z. 45 (1939), 335-367. | MR | Zbl
[5] Cecil T. E., Ryan P. J.: Tight and taut immersions of manifolds. Research Notes in Math., Pitman 1985. | MR | Zbl
[6] Chang S.: A closed hypersurface with constant scalar and mean curvature in $S^4$ is isoparametric. Comm. Anal. Geom. (1) 1 (1993), 71-100. | MR
[7] Ferus D.: Notes on isoparametric hypersurfaces. Escola de Geometria Diferencial, Universidade Estadual de Campinas, 1980.
[8] Ferus D., Karcher H., Münzner H. F.: Clifford algebren und neue isoparametrische hyperflächen. Math. Z. (1981), 479-502.
[9] 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. | MR
[10] Ozeki H., Takeuchi M.: On some types of isoparametric hypersurfaces in spheres, I. Tôhoku Math. J. 27 (1975), 515-559. | MR | Zbl
[11] Ozeki H., Takeuchi M.: On some types of isoparametric hypersurfaces in spheres, I. Tôhoku Math. J. 28 (1976), 7-55. | MR
[12] Sekigawa K.: On some $3$-dimensional Riemannian manifolds. Hokkaido Math. J. 26 (1974), 259-270. | MR
[13] Singer I. M.: Infinitesimally homogeneous spaces. Comm. Pure Appl. Math. 13 (1960), 685-697. | MR | Zbl
[14] Takagi H.: On curvature homogeneity of Riemannian manifolds. Tôhoku Math. J. 26 (1974), 581-585. | MR | Zbl
[15] Tricerri F., Vanhecke L.: Cartan hypersurfaces and reflections. Nihonkai Math. J. (2) 1 (1990), 203-208. | MR | Zbl
[16] Tsukada K.: Curvature homogeneous hypersurfaces immersed in a real space form. Tôhoku Math. J. 40 (1988), 221-244. | MR | Zbl
[17] Yamada A.: Homogeneity of hypersurfaces in a sphere. Tsukuba J. Math. 22 (1) (1998), 131-143. | MR | Zbl
[18] Yamato K.: A characterization of locally homogeneous Riemann manifolds of dimension $3$. Nagoya Math. J. 123 (1991), 77-90. | MR | Zbl