A geometric classification of positively curved symmetric spaces and the isoparametric construction of the Cayley plane
On the Geometry of Differentiable Manifolds Rome, 23-27 juin 1986, Astérisque, no. 163-164 (1988), pp. 111-135. 
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     author = {Karcher, Hermann},
     title = {A geometric classification of positively curved symmetric spaces and the isoparametric construction of the {Cayley} plane},
     booktitle = {On the Geometry of Differentiable Manifolds Rome, 23-27 juin 1986},
     series = {Ast\'erisque},
     pages = {111--135},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {163-164},
     year = {1988},
     zbl = {0669.53038},
     language = {en},
     url = {http://archive.numdam.org/item/AST_1988__163-164__111_0/}
}
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Karcher, Hermann. A geometric classification of positively curved symmetric spaces and the isoparametric construction of the Cayley plane, dans On the Geometry of Differentiable Manifolds Rome, 23-27 juin 1986, Astérisque, no. 163-164 (1988), pp. 111-135. http://archive.numdam.org/item/AST_1988__163-164__111_0/

[Ab] Abresch, U. : Isoparametric hypersurfaces with four or six different principal curvatures. Necessary conditions on the multiplicities. Math. Ann. 264 (1983), 283-302. | DOI | EuDML | Zbl

[AW] Aloff, S., Wallach, N. L. : An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures. Bull. Amer. Math. Soc. 81 (1975), 93-97. | DOI | Zbl

[Be] Berard Bergery, L. : Les variétés Riemanniennes homogènes simplement connexes de dimension impaire à courbure strictement positive. J. Math. Pures Appl. 55 (1976), 47-68. | Zbl

[Bg] Berger, M. : Les variétés Riemanniennes homogènes normales simplement connexes à courbure strictement positive. Ann. Scuola Norm. Sup. Pisa 15 (1961), 179-246. | EuDML | Numdam | Zbl

[BDG] Bombiéri, E., De Giorgi, E., Guisti, E. : Minimal cones and the Bernstein problem. Invent. Math. 7, 243-268 (1969). | DOI | EuDML | Zbl

[Ca] Cartan, E. : Sur des familles remarquables d'hypersurfaces isoparamétriques dans les espaces sphériques. Math. Z. 45 (1939), 335-367. | DOI | EuDML | JFM

[Ch] Chavel, I. : On Riemannian symmetric spaces of rank 1. Advances in Mathematics, Vol. 4, N° 3 (1970), 236- | DOI | Zbl

[Ci] Chi, Quo-Shin : Curvature properties of rank 1 symmetric spaces. Thesis Stanford June 1986.

[Es] Eschenburg, J.-H. : Freie isometrische Aktionen auf kompakten Lie-Gruppen mit positiv gekrümmten Orbiträumen. Schriften Math. Inst. Univ. Münster 2. Serie Hoft 32, 1-177. | Zbl

[Fe] Ferus, D. : Notes on isoparametric hypersurfaces. IMPA Lecture Notes (1980).

[FKM] Ferus, D., Karcher, H., Münsner, H.-F. : Cliffordalgebren und neue isoparametrische Hyperflächen. Math. Z. 177 (1981), 479-502. | DOI | EuDML | Zbl

[FK] Ferus, D., Karcher, H. : Non-rotational minimal spheres and minimizing cones. Comment. Math. Helv. 60 (1985), 247-269. | DOI | EuDML | Zbl

[GWZ] Gluck, H., Warner, F., Ziller, W. : The geometry of the Hopf fibrations. Preprint Univ. Penns., Aug. 1984. | Zbl

[He] Helgason, S. : Differential Geometry and Symmetric Spaces. Academic Press, New York 1962. | Zbl

[HL] Hsiang, W.-Y., Lawson, H. B. : Minimal submanifolds of low cohomogeneity. J. Dif. Geom. 5 (1971), 1-38. | DOI | Zbl

[Hs1] Hsiang, W.-Y. : Generalized rotational hypersurfaces of constant mean curvature in the euclidean spaces I. J. Dif. Geom. 17 (1982), 337-356. | DOI | Zbl

[Hs2] Hsiang, W.-Y. : Minimal cones and the spherical Bernstein problem. I. Annals of Math. 118 (1983), 61-73. | DOI | Zbl

Hsiang, W.-Y. : Minimal cones and the spherical Bernstein problem. II. Invent. Math. 74 (1983), 351-369. | DOI | EuDML | Zbl

[HS] Hsiang, W.-Y., Sterling, I. : Minimal cones and the spherical Bernstein problem III. Univ. of Cal. Berkeley preprint 236 (1984). | Zbl

[HHS] Hsiang, W.-T., Hsiang, W. Y., Sterling, I. : On the construction of codimension two minimal immersions of exotic spheres into Euclidean spheres. Invent. Math. 82 (1985), 447-460. | DOI | EuDML | Zbl

[HT] Hsiang, W.-Y., Tompter, P. : On the existence of infinitely many mutually non-congruent minimal immersions of S n-1 into S n (1),n≥4. To appear.

[La] Lawson, B. L. : The equivariant Plateau problem and interior regularity. Trans. A.M.S. 173 (1972), 231-249. | DOI | Zbl

[Mü] Münzner, H.-F. : Isoparametische Hyperflächen in Sphären Math. Ann. 251 (1980), 57-71. | DOI | EuDML

Münzner, H.-F. : Uber die Zerlegung der Sphäre in Ballbündel. Math. Ann. 256 (1981), 215-232. | EuDML | Zbl

[No] Nomizu, K. : Some results in E. Cartan's theory of isoparametric families of hypersurfaces. Bull. Amer. Math. Soc. 79 (1973), 1184-1189. | DOI | Zbl

[OT] Ozeki, H., Takeuchi, M. : On some types of isoparametric hyper-surfaces in spheres I. Tôhoku Math. J. 27 (1975), 515-559. | DOI | Zbl

[St] Sterling, I. : New examples of embedded spherical soap bubbles in S n (1). To appear. | Zbl

[TT] Takagi, R., Takahashi, T. : On the principal curvatures of homogeneous hypersurfaces in a sphere, 469-481. In : Differential Geometry in honor of K. Yano. Edited by Kobayashi, S., Obata, M., Takahashi, V., Tokyo 1972. | Zbl

[To] Tompter, P. : The spherical Bernstein problem in even dimensions. Preprint Oslo Math. Inst. 1983. | Zbl

[TV] Tricerri, F., Vanhecke, L. : Variétés Riemanniennes dont le tenseur de courbure est celui d'un espace symétrique riemannien irréductible. C.R. Acad. Sc. Paris, t. 302, Série I, N° 6 (1986) 233-235. | Zbl

[Wa] Walter, R. : Compact hypersurfaces with a constant higher mean curvature function. Math. Ann. 270 (1985), 125-145. | DOI | EuDML | Zbl

[W1] Wallach, N. L. : Compact homogeneous Riemannian manifolds with strictly positive curvature. Ann. of Math. 96 (1972), 277-295. | DOI | Zbl

[Wg] Wang, Qi-Ming : On the topology of Clifford isoparametric hy-persurfaces. To appear. | Zbl