On the existence of minimal hyperspheres in compact symmetric spaces

Wu-teh Hsiang; Wu-yi Hsiang; Per Tomter

Annales scientifiques de l'École Normale Supérieure (1988)

  • Volume: 21, Issue: 2, page 287-305
  • ISSN: 0012-9593

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Hsiang, Wu-teh, Hsiang, Wu-yi, and Tomter, Per. "On the existence of minimal hyperspheres in compact symmetric spaces." Annales scientifiques de l'École Normale Supérieure 21.2 (1988): 287-305. <http://eudml.org/doc/82228>.

@article{Hsiang1988,
author = {Hsiang, Wu-teh, Hsiang, Wu-yi, Tomter, Per},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {equivariant geometry; minimal hyperspheres; symmetric spaces},
language = {eng},
number = {2},
pages = {287-305},
publisher = {Elsevier},
title = {On the existence of minimal hyperspheres in compact symmetric spaces},
url = {http://eudml.org/doc/82228},
volume = {21},
year = {1988},
}

TY - JOUR
AU - Hsiang, Wu-teh
AU - Hsiang, Wu-yi
AU - Tomter, Per
TI - On the existence of minimal hyperspheres in compact symmetric spaces
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1988
PB - Elsevier
VL - 21
IS - 2
SP - 287
EP - 305
LA - eng
KW - equivariant geometry; minimal hyperspheres; symmetric spaces
UR - http://eudml.org/doc/82228
ER -

References

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  1. [1] É. CARTAN, Sur une classe remarquable d'espaces de Riemann (Bull. Soc. Math. Fr., Vol. 54, 1926, pp. 214-264 ; Vol. 55, 1927, pp. 964-1029). Zbl53.0390.01JFM53.0390.01
  2. [2] É. CARTAN, La géométrie des groupes de transformations (J. Math. Pures Appl., Vol. 6, 1927, pp. 1-119). Zbl53.0388.01JFM53.0388.01
  3. [3] S. S. CHERN, Differential geometry, its past and its future (Actes Cong. Intern. Math., Vol. 1, 1970, pp. 41-53). Zbl0232.53001MR55 #1242
  4. [4] D. FERUS and H. KARCHER, Non-rotational minimal spheres and minimizing cones (Comment. Math. Helv., Vol. 60, 1985, pp. 247-269). Zbl0566.53052MR87a:53097
  5. [5] W. T. HSIANG and W. Y. HSIANG, On the existence of codimension one minimal spheres in compact symmetric spaces of rank 2, II (J. of Differ. Geom., Vol. 17, 1982, pp. 583-594). Zbl0503.53044MR84a:53057
  6. [6] W. T. HSIANG, W. Y. HSIANG and P. TOMTER, On the construction of infinitely many, mutually noncongruent examples of minimal imbeddings of S²n-1 into CPn, n ≧ 2 (Bull. A.M.S., Vol. 8, 1983, pp. 463-465). Zbl0509.53047MR85a:53048
  7. [7] W. Y. HSIANG, Minimal cones and the spherical Bernstein problem, I (Ann. of Math., Vol. 118, 1983, pp. 61-73 ; II, Invent. Math., Vol. 74, 1983, pp. 351-369. Zbl0522.53051
  8. [8] W. Y. HSIANG and B. H. LAWSON Jr., Minimal submanifolds of low cohomogeneity (J. Differen. Geom., Vol. 5, 1971, pp. 1-38). Zbl0219.53045MR45 #7645
  9. [9] W. Y. HSIANG and I. STERLING, Minimal cones and the spherical Bernstein problem, III (Invent. Math., Vol. 85, 1986, pp. 223-247). Zbl0615.53054MR87k:53139
  10. [10] W. Y. HSIANG and P. TOMTER, On minimal immersions of Sn-1 into Sn(1), n ≧ 4 (Ann. Scient. E.N.S., Vol. 20, 1987, pp. 201-214). Zbl0627.53049MR88m:53111
  11. [11] J. SIMONS, Minimal varieties in Riemannian manifolds (Ann. of Math., Vol. 88, 1968, pp. 62-105). Zbl0181.49702MR38 #1617
  12. [12] P. TOMTER, The spherical Bernstein problem in even dimensions and related problems to appear in Acta Math.) Zbl0631.53047

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