Twistorial construction of harmonic maps of surfaces into four-manifolds
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 12 (1985) no. 4, pp. 589-640.
@article{ASNSP_1985_4_12_4_589_0,
     author = {Eells, J. and Salamon, S.},
     title = {Twistorial construction of harmonic maps of surfaces into four-manifolds},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {589--640},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 12},
     number = {4},
     year = {1985},
     mrnumber = {848842},
     zbl = {0627.58019},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1985_4_12_4_589_0/}
}
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Eells, J.; Salamon, S. Twistorial construction of harmonic maps of surfaces into four-manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 12 (1985) no. 4, pp. 589-640. http://archive.numdam.org/item/ASNSP_1985_4_12_4_589_0/

[A] Almgren F.J., Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem, Ann. of Math., 84 (1966), pp. 277-292. | MR | Zbl

[AHS] Atiyah M.F. - Hitchin N.J. - Singer I.M.: Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. Lond. Ser. A, 362 (1978), pp. 425-461. | MR | Zbl

[B] Berger M., Les variétés riemanniennes homogènes normales simplement connexes à courbure strictement positive, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 15 (1961), pp. 179-246. | EuDML | Numdam | MR | Zbl

[Be] Sém. A. Besse (1978-79), Géométrie riemannienne en dimension 4, Cedic/ F. Nathan (1981). | MR

[BH] Borel A. - Hirzebruch F., Characteristic classes and homogeneous spaces I, Amer. J. Math., 80 (1958), pp. 458-538. | MR | Zbl

[Br] Bryant R.L., Conformal and minimal immersions of compact surfaces into the 4-sphere, J. Differential Geom., 17 (1982), pp. 455-473. | MR | Zbl

[Bu] Burstall F.E., Non-linear functional analysis and harmonic maps, Ph. D. Thesis, University of Warwick (1984).

[C1] Calabi E., Minimal immersions of surfaces in Euclidean spheres, J. Differential Geom., 1 (1967), pp. 111-125. | MR | Zbl

[C 2] Calabi E., Quelques applications de l'analyse complexe aux surfaces d'aire minima. Topics in Complex Manifolds, Univ. de Montréal (1967), pp. 59-81.

[Ch1] Chern S.S., Minimal surfaces in Euclidean space of N dimensions, in Differential and Combinatorial Topology: Symposium in honor of Marston Morse, Princeton University Press (1965), pp. 187-198. | MR | Zbl

[Ch 2] Chern S.S., On the minimal immersions of the two-sphere in a space of constant curvature. Problems in Analysis, Princeton University Press (1970), pp. 27-40. | MR | Zbl

[CW] Chern S.S. - Wolfson J.G., Minimal surfaces by moving frames, Amer. J. Math., 105 (1983), pp. 59-83. | MR | Zbl

[E 1] Eells J., Gauss maps of surfaces, in Perspectives in Mathematics, Anniversary of Oberwolfach 1984, Birkhäuser. | MR | Zbl

[E 2] Eells J., Minimal branched immersions into three-manifolds, to appear. | MR

[EL] Eells J. - Lemaire L., A report on harmonic maps, Bull. London Math. Soc., 10 (1978), pp. 1-68. | MR | Zbl

[ES] Eells J. - Salamon S., Constructions twistorielles des applications harmoniques, C. R. Acad. Sci. Paris, 296 (1983), pp. 685-687. | MR | Zbl

[ESa] Eells J. - Sampson J.H., Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86 (1964), pp. 109-160. | MR | Zbl

[EW1] Eells J. - Wood J.C., Maps of minimum energy, J. London Math. Soc., 23 (1981), pp. 303-310. | MR | Zbl

[EW2] Eells J. - Wood J.C., Harmonic maps from surfaces to complex projective spaces, Adv. in Math., 49 (1983), pp. 217-263. | MR | Zbl

[ETG] Eschenburg J.H. - Tribuzy R. De A. - Guadalupe I.V., The fundamental equations of minimal surfaces in CP2, Math. Ann., 270 (1985), pp. 571-598. | MR | Zbl

[F] Friedrich T., On surfaces in four-spaces, Ann. Glob. Analysis and Geometry, 2 (1984), pp. 257-287. | MR | Zbl

[G1] Gray A., Minimal varieties and almost Hermitian manifolds, Michigan Math. J., 12 (1965), pp. 273-287. | MR | Zbl

[G2] Gray A., Riemannian manifolds with geodesic symmetries of order 3, J. Differential Geom., 7 (1972), pp. 343-369. | MR | Zbl

[GOR] Gulliver R.D. - Osserman R. - Royden H.L., A theory of branched immersions of surfaces, Amer. J. Math., 95 (1973), pp. 750-812. | MR | Zbl

[Hi] Hirsch M.W., Immersions of manifolds, Trans. Amer. Math. Soc., 93 (1959), pp. 242-276. | MR | Zbl

[Hir] Hirzebruch F., Topological Methods in Algebraic Geometry, 3rd edition, Springer, 1966. | MR | Zbl

[H 1] Hitchin N.J., Compact four-dimensional Einstein manifolds, J. Differential Geometry, 9 (1974), pp. 435-441. | MR | Zbl

[H2] Hitchin N.J., Kählerian twistor spaces, Proc. London Math. Soc., 43 (1981), pp. 133-150. | MR | Zbl

[H3] Hitchin N.J., Monopoles and geodesics, Comm. Math. Phys., 83 (1982), pp. 579-602. | MR | Zbl

[K] Kodaira K., On the structure of compact complex analytic surfaces II, Amer. J. Math., 88 (1966), pp. 682-721. | MR | Zbl

[KM] Koszul J.-L. - Malgrange B., Sur certaines structures fibrées complexes, Arch. Math., 9 (1958), pp. 102-109. | MR | Zbl

[LS] Lashof R. - Smale S., On the immersion of manifolds in Euclidean space, Ann. Math., 68 (1958), pp. 562-583. | MR | Zbl

[L1] Lawson H.B., Complete minimal surfaces in S3, Ann. of Math., 92 (1970), pp. 335-374. | MR | Zbl

[L 2] Lawson H.B., Lectures on Minimal Submanifolds, 2nd edition, Publish or Perish, 1980. | MR | Zbl

[Le] Lebrun C.R., Twistor CR manifolds and 3-dimensional conformal geometry, Trans. Amer. Math. Soc. 284 (1984), pp, 601-616. | MR | Zbl

[Li] Lichnerowicz A., Applications harmoniques et variétés kählériennes, Symposia Mathematica, 3 (1970), pp. 341-402. | MR | Zbl

[M] Micallef M.J., Stable minimal surfaces in Euclidean space, J. Differential Geom., 19 (1984), pp. 57-84. | MR | Zbl

[N] Naitoh H., Isotropic submanifolds with parallel second fundamental form in pm(c), Osaka J. Math., 18 (1981), pp. 427-464. | MR | Zbl

[NN] Newlander A. - Nirenberg L., Complex analytic coordinates in almost complex manifolds, Ann. of Math., 65 (1957), pp. 391-404. | MR | Zbl

[NW] Nijenhuis A. - Woolf W.B., Some integration problems in almost-complex and complex manifolds, Ann. of Math., 77 (1963), pp. 424-489. | MR | Zbl

[O] Obata M., The Gauss map of immersions of Riemannian manifolds in spaces of constant curvature, J. Differential Geom., 2 (1968), pp. 217-223. | MR | Zbl

[ON] O'Neill B., The fundamental equations of a submersion, Michigan Math. J., 13 (1966), pp. 459-469. | MR | Zbl

[P] Poon Y.S., Minimal surfaces in four-dimensional manifolds, M. Sc. Thesis, University of Oxford, 1983.

[R] Rawnsley J.H., f-structures, f-twistor spaces and harmonic maps, in Geometry Seminar Luigi Bianchi II, to appear. | MR | Zbl

[Ru] Ruh E.A., Minimal immersions of 2-spheres in S4, Proc. Amer. Math. Soc., 28 (1971), pp. 219-222. | MR | Zbl

[RV] Ruh E.A. - Vilms J., The tension field of the Gauss map, Trans. Amer. Math. Soc., 149 (1970), pp. 569-573. | MR | Zbl

[S1] Salamon S., Quaternionic Kähler manifolds, Invent. Math., 67 (1982), pp. 143-171. | MR | Zbl

[S 2] Salamon S., Topics in four-dimensional Riemannian geometry, in Geometry Seminar Luigi Bianchi, Lecture Notes in Mathematics 1022, Springer (1983), pp. 33-124. | MR | Zbl

[S 3] Salamon S., Harmonic and holomorphic maps, in Geometry Seminar Luigi Bianchi II, to appear. | MR | Zbl

[Sm] Smale S., A survey of some recent developments in differential topology, Bull. Amer. Math. Soc., 69 (1963), pp. 131-145. | MR | Zbl

[SU] Sacks J. - Uhlenbeck K., The existence of minimal immersions of two-spheres, Ann. of Math., 113 (1981), pp. 1-24. | MR | Zbl

[W] Wolf J.A., Complex homogeneous contact manifolds and quaternionic symmetric spaces, J. Math. Mech., 14 (1965), pp. 1033-1047. | MR | Zbl

[WG] Wolf J.A. - Gray A., Homogeneous spaces defined by Lie group automorphisms I, II, J. Differential Geom., 2 (1968), pp. 77-159. | MR | Zbl

[Wo] Wolfson J.G., Minimal surfaces in complex manifolds, Ph. D. Thesis, University of California Berkley (1982).

[GL] Gauduchon P. - Lawson H.B., Topologically nonsingular minimal cones. | Zbl

[Gr] Gromov, M., Pseudo holomorphic curves in symplectic manifolds. | Zbl

[We] Webster S.M., Minimal surfaces in a Kähler surface. | Zbl