Tohoku Mathematical Journal

Homogeneous minimal hypersurfaces in the unit spheres and the first eigenvalues of their Laplacian

Hideo Mutō, Yoshihiro Ohnita, and Hajime Urakawa

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Tohoku Math. J. (2), Volume 36, Number 2 (1984), 253-267.

First available in Project Euclid: 3 May 2007

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Zentralblatt MATH identifier

Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 35P15: Estimation of eigenvalues, upper and lower bounds 58G25


Mutō, Hideo; Ohnita, Yoshihiro; Urakawa, Hajime. Homogeneous minimal hypersurfaces in the unit spheres and the first eigenvalues of their Laplacian. Tohoku Math. J. (2) 36 (1984), no. 2, 253--267. doi:10.2748/tmj/1178228851.

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  • [1] S. ARAKI, On root systems and an infinitesimal classification of irreducible symmetric spaces, J. Math. Osaka City Univ. 13 (1962), 1-34.
  • [2] M. BERGER, P. GAUDUCHON AND E. MAZET, Le spectre d'une variete riemannienne, Lectur Notes in Math. 194, Springer-Verlag, Berlin, Heidelberg, New York, 1971.
  • [3] T. HASEGAWA, Spectral geometry of closed minimal submanifolds in a space form, rea or complex, Kdai Math. J. 3 (1980), 224-252.
  • [4] S. HELGASON, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962.
  • [5] W. Y. HSIANG AND H. B. LAWSON, JR., Minimal submanifolds of low cohomogeneity, J. Differential Geom. 5 (1971), 1-36.
  • [6] H. MUTO, The multiplicity of the first eigenvalue of the Laplacian on SU(2), S0(3) an l)/Sp(w), preprint.
  • [7] H. MUTO AND H. URAKAWA, On the least positive eigenvalue of Laplacian for compac homogeneous spaces, Osaka J. Math. 17 (1980), 471-484.
  • [8] H. F. MUNZNER, Isoparametrische Hyperflachen in Spharen, Math. Ann. 251 (1981), 57-71
  • [9] H. F. MUNZNER, Isoparametrische Hyperflasehen in Spharen, II, Math. Ann. 256 (1981), 215-232.
  • [10] K. OGIUE, Open Problems, Surveys in Geometry, 1980/1981, Geometry of the Laplac Operator, edited by T. Ochiai, (in Japanese).
  • [11] J. SIMONS, Minimal varieties in Riemannian manifolds, Ann. of Math. 88 (1968), 62-105
  • [12] M. SUGIURA, Spherical functions and representation theory of compact Lie groups, Sci Papers College Gen. Ed. Univ. Tokyo 10 (1960), 187-193.
  • [13] T. TAKAHASHI, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 1 (1966), 380-385.
  • [14] R. TAKAGI AND T. TAKAHASHI, On the principal curvatures of homogeneous hypersurface in a unit sphere, Dif. Geometry, in honor of K. Yano, Kinokuniya, Tokyo, 1972, 469-481.
  • [15] M. TAKEUCHI, Modern Theory of Spherical Functions (in Japanese), Iwanami, Tokyo, 1975.
  • [16] M. TAKEUCHI AND S. KOBAYASHI, Minimal imbeddings of ^-spaces, J. Differential Geom 2 (1968), 203-215.
  • [17] S. YAMAGUCHI, Spectra of flag manifolds, Mem. Fac. Sci. Kyushu Univ. 33 (1979), 95-112
  • [18] S. T. YAU, Problem Section, Seminar on Differential Geometry, Ann. Math. Studies 102, Princeton Univ. Press, 1982, p. 692.