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REFERENCES
M. Berger, Geometry I-II, Springer, New York, 1977.
E. Calabi, Minimal immersions of surfaces in euclidean spheres, J. Diff. Geom. 1 (1967) 111–125.
D. DeTurck and W. Ziller, Spherical minimal immersions of spherical space forms, Proc. of Symp. in Pure Math. 54 Part I (1993) 111–458.
D. DeTurck and W. Ziller, Minimal isometric immersions of spherical space forms in spheres, Comment. Math. Helvetici 67 (1992) 428–458.
F. Dillen, L. Verstraelen and L. Vrancken, Classification of totally real 3-dimensional submanifolds of S 6(1) with K e 1/16 , J. Math. Soc. Japan. (to appear).
M. DoCarmo and N. Wallach, Minimal immersions of spheres into spheres, Ann. of Math. 93 (1971) 43–62.
J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964) 109–160.
N. Ejiri, Totally real submanifods in a 6-sphere, Proc. Amer. Math. Soc. 83 (1981) 759–763.
C. M. Escher, Minimal isometric immersions of inhomogeneous spherical space forms into spheres — A necessary condition for existence, Trans. Amer. Math. Soc. 348, No. 9, (1996) 3713–3732.
C. M. Escher and G. Weingart, Orbits of SU(2)-representations and minimal isometric immersions, Math. Ann. 316 (2000) 743–769.
H. Gauchman and G. TÓth, Fine structure of the space of spherical minimal immersions, Trans. Amer. Math. Soc. 348, No. 6 (1996) 2441–2463.
F. Klein, Lectures on the Icosahedron, and the Solution of Equations of the Fifth Degree, Trübner and Co., 1888.
K. Mashimo, Minimal immersions of 3-dimensional spheres into spheres, Osaka J. Math. 2 (1984) 721–732.
K. Mashimo, Homogeneous totally real submanifolds in S 6, Tsukuba J. Math. 9 (1985) 185–202.
J. D. Moore, Isometric immersions of space forms into space forms, Pacific J. Math. 40 (1976) 157–166.
Y. Muto, The space W 2 of isometric minimal immersions of the three-dimensional sphere into spheres, Tokyo J. Math. 7 (1984) 337–358.
R. T. Smith, Harmonic mappings of spheres, Thesis, Warwick University (1980).
T. Takahashi, Minimal immersions of Riemannian manifolds, J Math. Soc. Japan 18 (1966) 380–385.
G. TÓth, Geometry of the moduli space for eigenmaps and spherical minimal immersions, Preprint, 2000.
G. TÓth, Infinitesimal rotations of isometric minimal immersions between spheres, Amer. J. Math. 122 (2000) 117–152.
G. TÓth, Universal constraints on the range of eigenmaps and spherical minimal immersions, Trans. Amer. Math. Soc. 351 No. 4 (1999) 1423–1443.
G. TÓth, Eigenmaps and the space of minimal immersions between spheres, Indiana Univ. Math. J. 46 No. 2 (1997) 637–658.
G. TÓth, Rigidity of minimal submanifolds in terms of higher fundamental forms, Michigan Math. J. 40 No. 3 (1993) 493–505.
G. TÓth, Operators on eigenmaps between spheres, Compositio Mathematica 88 (1993) 317–332.
G. TÓth, Mappings of moduli spaces for harmonic eigenmaps and minimal immersions between spheres, J. Math. Soc. Japan 44, No. 2 (1992) 179–198.
G. TÓth, Harmonic Maps and Minimal Immersions through Representation Theory, Academic Press, Boston, 1990.
G. TÓth and W. Ziller, Spherical minimal immersions of the 3-sphere, Comment. Math. Helv. 74 (1999) 1–34.
N. I. Vilenkin, Special Functions and the Theory of Group Representations, AMS Translations of Mathematical Monographs 22, 1968.
N. Wallach, Minimal immersions of symmetric spaces into spheres, in Symmetric Spaces, Dekker, New York (1972) 1–40.
G. Weingart, Geometrie der Modulräume minimaler isometrischer Immersionen der Sphären in Sphären, Bonner Mathematische Schriften, Nr. 314, Bonn (1999).
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Tóth, G. Minimal Immersions of Spheres and Moduli. Periodica Mathematica Hungarica 40, 211–227 (2000). https://doi.org/10.1023/A:1010347812215
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DOI: https://doi.org/10.1023/A:1010347812215