Closed hypersurfaces of S 4 with two constant symmetric curvatures

Sebastião Carneiro de Almeida; Fabiano Gustavo Braga Brito

Annales de la Faculté des sciences de Toulouse : Mathématiques (1997)

  • Volume: 6, Issue: 2, page 187-202
  • ISSN: 0240-2963

How to cite


Carneiro de Almeida, Sebastião, and Gustavo Braga Brito, Fabiano. "Closed hypersurfaces of $S^4$ with two constant symmetric curvatures." Annales de la Faculté des sciences de Toulouse : Mathématiques 6.2 (1997): 187-202. <>.

author = {Carneiro de Almeida, Sebastião, Gustavo Braga Brito, Fabiano},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {isoparametric hypersurfaces of the 4-sphere; constant curvature},
language = {eng},
number = {2},
pages = {187-202},
title = {Closed hypersurfaces of $S^4$ with two constant symmetric curvatures},
url = {},
volume = {6},
year = {1997},

AU - Carneiro de Almeida, Sebastião
AU - Gustavo Braga Brito, Fabiano
TI - Closed hypersurfaces of $S^4$ with two constant symmetric curvatures
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1997
VL - 6
IS - 2
SP - 187
EP - 202
LA - eng
KW - isoparametric hypersurfaces of the 4-sphere; constant curvature
UR -
ER -


  1. [AD] Alencar ( H.) and Do Carmo ( M.) .— Hypersurfaces with constant mean curvature in spheres, Proc. Amer. Math. Soc.120 (1994), pp. 1223-1229. Zbl0802.53017MR1172943
  2. [AB1] De Almeida ( S.C.) and Brito ( F.G.B.).— Minimal hypersurfaces of S4 with constant Gauss—Kronecker curvature, Math. Z.195 (1987), pp. 99-107. Zbl0602.53040MR888131
  3. [AB2] De Almeida ( S.C.) and Brito ( F.G.B.). — Closed 3-dimensional hypersurface with constant mean curvature and constant scalar curvature, Duke Math. J.61 (1990), pp. 195-206. Zbl0721.53056MR1068385
  4. [BD] Barbosa ( J.L.M.) and Delgado ( J.A.) .— Ruled submanifolds of space forms with mean curvature of nonzero constant length, American Journal of Mathematics, 106 (1984), pp. 763-780. Zbl0553.53010MR749256
  5. [Ca] Cartan ( E.) .— Familles de surfaces isoparamétriques dans les espaces à courbure constante, Annali di Mat.17 (1938), pp. 177-191. Zbl0020.06505MR169JFM64.1361.02
  6. [C] Chang ( S.). — A closed hypersurface with constant scalar curvature and mean curvature in S4 is isoparametric, Communications in Analysis and Geometry, 1, n° 1 (1993), pp. 71-100. Zbl0791.53058MR1230274
  7. [CDK] Chern ( S.S.), Do Carmo ( M.) and Kobayashi ( S.) .— Minimal submanifolds of the sphere with second fundamental form of constant length, Functional analysis and related fields, pp. 59-75 (ed. F. Browder), BerlinHeidelbergNew York, Springer, 1970. Zbl0216.44001MR273546
  8. [H] Hsiang ( Wu Yi).— Minimal cones and the spherical Bernstein problem, I, Ann. of Math.118 (1983), p. 61-73. Zbl0522.53051MR707161
  9. [L] Lawson ( H.B. Jr).— Minimal Varieties in Real and Complex Geometry, Séminaire de Mathématiques Supérieures, Département de Mathématiques — Université de Montréal (1974). Zbl0328.53001MR474148
  10. [PT1] Peng ( C.K.) and Terng ( C.L.).— Minimal hypersurfaces of spheres with constant scalar curvature, Seminar on minimal submanifolds (ed. E. Bombieri), Ann. Math. Stud.103 (1983), Princeton Univ. Press, pp. 177-198. Zbl0534.53048MR795235
  11. [PT2] Peng ( C.K.) and Terng ( C.L.). — The scalar curvature of minimal hypersurfaces in spheres, Math. Ann.266 (1983), pp. 105-113. Zbl0508.53060MR722930
  12. [R] Ramanathan ( J.) .— Minimal hypersurfaces in S4 with vanishing Gauss-Kronecker curvature, Math. Z.205 (1990), pp. 645-658. Zbl0694.53054MR1082881
  13. [W] Van Der Waerden ( B.L.). — Algebra, Vol. 1, Frederick Ungar Publishing Co., Inc. (1970). MR263582

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