Clifford systems, algebraically constant second fundamental form and isoparametric hypersurfaces

Manuscripta Mathematica

Volumn 97, Issue 3, 1998, Pages 335-342

  Console, Sergio ^a   Olmos, Carlos ^b  

^a UNIVERSITY OF TURIN   (Italy)

^b UNIVERSIDAD NACIONAL DE CÓRDOBA   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032210303     PISSN: 00252611     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002290050106     Document Type: Article

References (18)

1. Cartan, É.: Sur des familles remarquables d'hypersurfaces isoparamétriques dans les éspaces spheriques. Math. Z. 45, 335-367 (1939)
2. Chern, S.M., do Carmo, S., Kobayashi, S.: Minimal Submanifolds of a Sphere with second fundamental form of constant Length. In: Functional Analysis and Related Fields, Springer, Berlin, 1970, pp. 59-75
3. Console, S., Olmos, C.: Submanifolds of higher rank. Quart. J. Math. Oxford (2) 48,309-321 (1997)
4. Ferus, D.: Symmetric submanifolds of Euclidean space. Math. Ann. 247, 81-93 (1980)
5. Ferus, D., Karcher, H. and Münzner, H.F.: Clifford Algebren und neue isoparametriche Hyperflächen. Math. Z. 177, 479-502 (1981)
6. Heintze, E., Olmos, C. and Thorbergsson, G.: Submanifolds with constant principal curvatures and normal holonomy groups. Int. J. Math. 2, 167-175 (1991)
7. Helgason, S.: Differential Geometry, Lie groups and symmetric spaces. Academic Press, New York, 1978
8. Hsiang W.-Y. and Lawson, B.H.: Minimal submanifolds of low cohomogeneity. J. Differ. Geom. 5, 1-38 (1971)
9. Karcher, H.: A geometric classification of positively curved symmetric spaces and the isoparametric construction of the Cayley plane. Astérisque 163-164, 111-135 (1988)
10. Knarr, N., Kramer, L.: Projective Planes and Isoparametric Hypersurfaces. Geometriae Dedicata 58, 193-202 (1995)
11. Lawson, B.H. and Michelson, M.: Spin Geometry. Princeton University Press, Princeton, N.J., 1990
12. Mercuri, F.: Parallel and semi-parallel immersions into space forms. Riv. Mat. Univ. Parma 17, 91-108 (1991)
13. Münzner, H.F.: Isoparametrische Hyperflächen in Sphären, I, II. Math. Ann. 251, 57-71 (1980); 256, 215-232 (1981)
14. Münzner, H.F.: Isoparametrische Hyperflächen in Sphären, I, II. Math. Ann. 251, 57-71 (1980); 256, 215-232 (1981)
15. Olmos, C.: Homogeneous submanifolds of higher rank and parallel mean curvature. J. Differ. Geom. 39, 605-627 (1994)
16. Palais, R. and Terng, C.-L.: Critical Point Theory and Submanifold Geometry. Lect. Notes in Math. 1353, Springer, Berlin Heidelberg New York, 1988
17. Reckziegel, H.: On the problem whether the image of a given differentiable map into a Riemannian manifold is contained in a submanifold with parallel second fundamental form. J. Reine Angew. Math. 325, 87-104 (1981)
18. Tricerri, F. and Vanhecke, L.: Curvature homogeneous Riemannian manifolds. Ann. Sc. Éc. Norm. Supér., I V Sér. 22, 535-554 (1989)