Tohoku Mathematical Journal

Eigenmaps and minimal immersions of projective spaces into spheres

Katsuya Mashimo

Full-text: Open access

Article information

Source
Tohoku Math. J. (2), Volume 40, Number 2 (1988), 245-267.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178228029

Digital Object Identifier
doi:10.2748/tmj/1178228029

Mathematical Reviews number (MathSciNet)
MR0943822

Zentralblatt MATH identifier
0648.53033

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 58E20: Harmonic maps [See also 53C43], etc.

Citation

Mashimo, Katsuya. Eigenmaps and minimal immersions of projective spaces into spheres. Tohoku Math. J. (2) 40 (1988), no. 2, 245--267. doi:10.2748/tmj/1178228029. https://projecteuclid.org/euclid.tmj/1178228029


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References

  • [1] F. A. BEREZIN, Laplace operators on semi-simple Lie groups, Trudy Moskov. Mat. Obsc. 6 (1957), 371-463.
  • [2] M. R. BREMNER, R. V. MOODY AND J. PATERA, Tables of Dominant Weight Multiplicitie for Representations of Simple Lie Algebras, Pure and Appl. Math. 90, Marcel Dekker, New York, 1985.
  • [3] M. P. DO CARMO AND N. R. WALLACH, Minimal immersions of spheres into spheres, Ann of Math. (2) 93 (1971), 43-62.
  • [4] M. GOTO AND F. D. GROSSHANS, Semisimple Lie Algebras, Lecture Notes in Pure an Appl. Math. 38, Marcel Dekker, New York, Basel, 1978.
  • [5] J. EELLS AND L. LEMAIRE, A report on harmonic maps, Bull. London Math. Soc. 1 (1978), 1-68.
  • [6] J. E. HUMPHREYS, Introduction to Lie Algebras and Representation Theory, Graduat Text in Math. 9, Springer Verlag, Berlin, Heidelberg, New York, 1970.
  • [7] K. MASHIMO, Spectra of Laplacian on FJSpin(9), in preparation
  • [8] R. T. SMITH, The spherical representations of groups transitive on Sn, Indiana Univ Math. J. 24 (1974), 307-325.
  • [9] T. TAKAHASHI, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 1 (1966), 380-385.
  • [10] M. TAKEUCHI, Modern Theory of Spherical Functions, (in Japanese), Iwanami-Shoten, Tokyo, 1957.
  • [11] G. TOTH, On non-rigidity of harmonic maps into spheres, preprint
  • [12] G. TOTH AND G. D'AMBRA, Parameter space for harmonic maps of constant energy densit into spheres, Geom. Dedicata 17 (1984), 61-67.
  • [13] C. TSUKAMOTO, The spectra of Laplaee-Beltrami operators on SO(n + 2)/SO(2)xSO(n) an Sp(n + D/Sp(l)xSp(n), Osaka J. Math. 18 (1981), 407-426.
  • [14] H. URAKAWA, Minimal immersions of protective spaces into spheres, Tsukuba J. Math 9 (1985), 321-347.
  • [15] L. VRETARE, Elementary spherical functions on symmetric spaces, Math. Scand. 39 (1976), 343-358.
  • [16] Z. YIMING, Minimal immersions of rank 1 compact symmetric spaces into spheres, Sci Sinica 28 (1985), 263-272.