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Münzner, Hans Friedrich

Isoparametrische Hyperflächen in Sphären. I. (German) Zbl 0417.53030

Math. Ann. 251, 57-71 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0417.53030

Cited in 13 Reviews
Cited in 120 Documents

MSC:

53C40 Global submanifolds

Keywords:

isoparametric hypersurface; principal curvature; critical points; focal sets

Citations:

Zbl 0318.53052; Zbl 0359.53011; Zbl 0359.53012
Cite Review PDF
Full Text: DOI EuDML

References:

[1] Cartan, E.: Familles de surfaces isoparam?triques dans les espaces ? courbure constante. Ann. Mat. Pura Appl.17, 177-191 (1938) · Zbl 0020.06505 · doi:10.1007/BF02410700
[2] Cartan, E.: Sur des familles remarquables d’hypersurfaces isoparam?triques dans les espaces spheriques. Math. Z.45, 335-367 (1939) · Zbl 0021.15603 · doi:10.1007/BF01580289
[3] Cartan, E.: Sur quelques familles remarquables d’hypersurfaces. C.P. Congr?s Math. Li?ge, pp. 30-41 (1939)
[4] Cartan, E.: Sur des familles remarquables d’hypersurfaces isoparam?triques des espaces sph?riques ?r et 9 dimensions. Rev. Unib. Tucoman AI, 5-22 (1940) · Zbl 0025.22603
[5] Husemoller, D.: Fibre bundles. New York: McGraw-Hill 1966 · Zbl 0144.44804
[6] Hsiang, W.Y.: Remarks on closed minimal submanifolds in the standard Riemannianm-sphere. J. Differential Geometry1, 257-267 (1967) · Zbl 0168.42904
[7] Hsiang, W.Y., Lawson, Jr., H.B.: Minimal submanifolds of low cohomogeneity. J. Differential Geometry5, 1-38 (1971) · Zbl 0219.53045
[8] Kobayashi, S., Nomizi, K.: Foundations of differential geometry. II. New York: Interscience 1969
[9] Levi-Civita, T.: Famiglie di superficie isoparametriche nell’ordinario spacio euclideo. Atti Accad. naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur26, 355-362 (1937) · Zbl 0018.08702
[10] Nomizu, K.: Some results in E. Cartan’s theory of isoparametric families of hypersurfaces. Bull. Amer. Math. Soc.79, 1184-1188 (1974) · Zbl 0275.53003 · doi:10.1090/S0002-9904-1973-13371-3
[11] Ozeki, H., Takeuchi, M.: On some types of isoparametric hyperfaces in spheres. I. T?hoku Math. J.27, 515-559 (1975); II. T?hoku Math. J.28, 7-55 (1976) · Zbl 0359.53011 · doi:10.2748/tmj/1178240941
[12] Spanier, E.H.: Algebraic topology. New York: McGraw-Hill 1966 · Zbl 0145.43303
[13] Segre, B.: Famiglie di ipersuperficie isoparametrische negli spazi euclidei ad un qualunque numero di demensioni. Atti Accad. naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur27, 203-207 (1938) · Zbl 0019.18403
[14] Takagi, R., Takahashi, T.: On the principal curvatures of homogeneous hypersurfaces in a sphere. Differential geometry, in honor of K. Yano, pp. 469-481, Tokyo: Kinokuniya 1972 · Zbl 0244.53042
[15] Wang, H.C.: Compact transformation group ofS n with an (n-1)-dimensional orbit. Amer. J. Math.82, 698-748 (1960) · Zbl 0134.19404 · doi:10.2307/2372936
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