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Harmonic maps from surfaces to complex projective spaces. (English) Zbl 0528.58007

##### MSC:
 58E20 Harmonic maps, etc. 30F15 Harmonic functions on Riemann surfaces
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##### References:
 [1] Atiyah, M.F; Hitchin, N.J; Singer, I.M, Self-duality in four-dimensional Riemannian geometry, (), 425-461 · Zbl 0389.53011 [2] Barbosa, J, On minimal immersions of S2 into S2m, Trans. amer. math. soc., 210, 75-106, (1975) [3] Borchers, H.J; Garber, W.D, Local theory of solutions for the O(2k + 1) σ-model, Comm. math. phys., 72, 77-102, (1980) · Zbl 0425.35083 [4] Borůvka, O, Sur LES surfaces représentées par LES fonctions sphériques de première espèce, J. math. pures appl. (9), 12, 337-383, (1933) · Zbl 0008.08203 [5] Calabi, E, Quelques applications de l’analyse complexe aux surfaces d’aire minima, (), 59-81 [6] Calabi, E, Minimal immersions of surfaces in Euclidean spheres, J. differential geom., 1, 111-125, (1967) · Zbl 0171.20504 [7] Catenacci, R; Reina, C, Algebraic classification of $$CP$$^{n} instanton solutions, Lett. math. phys., 5, 469-473, (1981) · Zbl 0533.14005 [8] Chen, B-Y; Nagano, T; Chen, B-Y; Nagano, T, Totally geodesic submanifolds of symmetric spaces I, II, Duke math. J., Duke math. J., 45, 405-425, (1978) · Zbl 0384.53024 [9] Chern, S.S, On the minimal immersions of the two-sphere in a space of constant curvature, (), 27-40 [10] Chern, S.S, On minimal spheres in the four sphere, (), 137-150, studies and essays presented to Y. W. Chen, Taiwan [11] Din, A.M; Zakrzewski, W.J, General classical solutions in the $$CP$$^{n−1} model, Nuclear phys. B, 174, 397-406, (1980) [12] Din, A.M; Zakrzewski, W.J, Properties of the general classical $$CP$$^{n−1} model, Phys. lett. B, 95, 419-422, (1980) [13] Din, A.M; Zakrzewski, W.J, Classical solutions in Grassmannian σ-models, Lett. math. phys., 5, 553-561, (1981) · Zbl 0521.58037 [14] Eells, J; Lemaire, L, A report on harmonic maps, Bull. London math. soc., 10, 1-68, (1978) · Zbl 0401.58003 [15] Eells, J; Lemaire, L, On the construction of harmonic and holomorphic maps between surfaces, Math. ann., 252, 27-52, (1980) · Zbl 0424.31009 [16] Eells, J; Sampson, J.H, Harmonic mappings of Riemannian manifolds, Amer. J. math., 86, 109-160, (1964) · Zbl 0122.40102 [17] Eells, J; Wood, J.C, Restrictions on harmonic maps of surfaces, Topology, 15, 263-266, (1976) · Zbl 0328.58008 [18] Eells, J; Wood, J.C, Maps of minimum energy, J. London math. soc., 23, 303-310, (1981) · Zbl 0432.58012 [19] Eells, J; Wood, J.C, The existence and construction of certain harmonic maps, (), 123-138, Rome · Zbl 0488.58008 [20] Glaser, V; Stora, R, Regular solutions of the $$CP$$^{n} models and further generalizations, (1980), preprint [21] Griffiths, P; Harris, J, Principles of algebraic geometry, (1978), Wiley-Interscience New York · Zbl 0408.14001 [22] Griffiths, P; Schmid, W, Locally homogeneous complex manifolds, Acta math., 123, 253-301, (1969) · Zbl 0209.25701 [23] Gunning, R.C, Lectures on vector bundles over Riemann surfaces, () · Zbl 0163.31903 [24] Gulliver, R.D; Osserman, R; Royden, H, A theory of branched immersions of surfaces, Amer. J. math., 95, 750-812, (1973) · Zbl 0295.53002 [25] Heinz, E; Hildebrandt, S, Some remarks on minimal surfaces in Riemannian manifolds, Comm. pure appl. math., 23, 371-377, (1970) · Zbl 0188.42102 [26] Helgason, S, A duality for symmetric spaces with applications to group representations, Advan. math., 5, 1-154, (1970) · Zbl 0209.25403 [27] Hirzebruch, F, Topological methods in algebraic geometry, () · Zbl 0138.42001 [28] Ishihara, T, The index of a holomorphic mapping and the index theorem, (), 169-174 · Zbl 0375.58011 [29] Ishihara, T, The harmonic Gauss map in a generalized sense, J. London math. soc. (2), 26, 104-112, (1982) · Zbl 0498.53041 [30] Kenmotsu, K; Kenmotsu, K, On compact minimal surfaces with nonnegative Gaussian curvature in a space of constant curvature I, II, Tôhoku math. J., Tôhoku math. J., 27, 291-301, (1975) · Zbl 0335.53047 [31] Kenmotsu, K, On minimal immersions of $$R$$^{2} into SN, J. math. soc. Japan, 28, 182-191, (1976) · Zbl 0335.53048 [32] Kobayashi, S; Nomizu, K, Foundations of differential geometry I, II, (1969), Wiley-Interscience New York · Zbl 0175.48504 [33] Koszul, J.L; Malgrange, B, Sur certaines structures fibrees complexes, Arch. math., 9, 102-109, (1958) · Zbl 0083.16705 [34] Lawson, H.B, Lectures on minimal surfaces, () [35] Lemaire, L, Applications harmoniques de surfaces riemanniennes, J. differential geom., 13, 51-78, (1978) · Zbl 0388.58003 [36] Lemaire, L, Harmonic nonholomorphic maps from a surface to a sphere, (), 299-304 · Zbl 0388.58004 [37] Leung, P-F, On the stability of harmonic maps, (), preprint 1981 [38] Lichnerowicz, A, Applications harmoniques et variétés kählériennes, (), 341-402, Bologna · Zbl 0193.50101 [39] Ludden, G-D; Okumura, M; Yano, K, A totally real surface in $$CP$$^{2} that is not totally geodesic, (), 186-190 · Zbl 0312.53043 [40] Narasimhan, M.S, Vector bundles on compact Riemann surfaces, (), 63-88 · Zbl 0369.32010 [41] Nishikaẃa, S, The Gauss map of Kähler immersions, Tôhoku math. J., 27, 453-460, (1975) · Zbl 0322.53026 [42] Obata, M, The Gauss map of immersions of Riemannian manifolds in spaces of constant curvature, J. differential geom., 2, 217-223, (1968) · Zbl 0181.49801 [43] O’Neill, B, The fundamental equations of a submersion, Michigan math. J., 13, 459-470, (1966) · Zbl 0145.18602 [44] Rund, H, Variational problems and Bäcklund transformations associated with the sine-Gordon and Korteweg-devries equations and their extensions, (), 119-226 [45] Sacks, J; Uhlenbeck, K, The existence of minimal immersions of the two-sphere, Ann. of math. (2), 113, 1-24, (1981) · Zbl 0462.58014 [46] Schmid, W, Variation of Hodge structure: singularities of the period mapping, Invent. math., 22, 211-319, (1973) · Zbl 0278.14003 [47] Semple, J.G; Roth, L, Introduction to algebraic geometry, (1949), Oxford Univ. Press (Clarendon) London/New York · Zbl 0041.27903 [48] Siu, Y.-T; Yau, S.-T, Compact Kähler manifolds of positive bisectional curvature, Invent. math., 59, 189-204, (1980) · Zbl 0442.53056 [49] Siu, Y.-T, Some remarks on the complex analyticity of harmonic maps, Southeast Asian bull. math., 3, 240-253, (1979) · Zbl 0439.53051 [50] Siu, Y.-T, The complex-analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds, Ann. of math., 112, 73-111, (1980) · Zbl 0517.53058 [51] Smith, R.T, Harmonic mappings of spheres, (), Amer. J. math., 97, 364-385, (1975) · Zbl 0321.57020 [52] Smith, R.T, The second variation formula for harmonic mappings, (), 229-236 · Zbl 0303.58008 [53] Suzuki, O, Theorems on holomorphic bisectional curvature and pseudoconvexity on Kähler manifolds, (), 412-428, Kozubnik [54] {\scO. Suzuki}, Pseudoconvexity and holomorphic bisectional curvature on Kähler manifolds, preprint. · Zbl 0437.53055 [55] Uhlenbeck, K, Minimal 2-spheres and tori in Sk, (1975), preprint [56] Uhlenbeck, K, Equivariant harmonic maps into spheres, (), 146-158 · Zbl 0505.58015 [57] Wood, J.C, Harmonic maps and complex analysis, (), 289-308, Trieste [58] Wood, J.C, Holomorphicity of certain harmonic maps from a surface to complex projective n-space, J. London math. soc., 20, 137-142, (1979) · Zbl 0407.58026 [59] Wood, J.C, On the holomorphicity of harmonic maps from a surface, (), Berlin/New York · Zbl 0437.58006 [60] Wood, J.C, Conformality and holomorphicity of certain harmonic maps, (1981), Univ. of Leeds, preprint [61] Wu, H.H, The equidistribution theory of holomorphic curves, Ann. of math. stud., 64, (1970) · Zbl 0199.40901 [62] Burns, D, Harmonic maps from $$CP$$^{l} to $$CP$$n, (), 48-56 · Zbl 0507.58018 [63] Catenacci, R; Cornalba, M; Reina, C, Classical solutions of $$CP$$^{n} model: an algebraic geometrical description, (1982), Univ. di Pavia, preprint · Zbl 0588.14007 [64] {\scS.-S. Chern and J. G. Wolfson}, Minimal surfaces by moving frames, preprint. · Zbl 0521.53050 [65] Eroem, S; Wood, J.C, On the construction of harmonic maps into a Grassmannian, J. London math. soc., (1983), (in press) · Zbl 0492.58013 [66] Rawnsley, J.H, Notes on homogeneous spaces, (1982), Univ. of Warwick, preprint · Zbl 0518.58019
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