This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
M. F. Atiyah, Instantons in two and four dimensions, Commun. Math. Phys. 93 (1984), 437–451.
M. F. Atiyah, N. J. Hitchin and I. M. Singer, Self-duality in four dimensional Riemannian geometry, Proc. R. Soc. London, A. 362 (1978), 425–461.
D. Barbasch, J. H. Glazebrook and G. Toth, Harmonic maps between complex projective spaces, to appear in Geom. Dedicata.
A. Bahy-El-Dien and J. C. Wood, The explicit construction of all harmonic two-spheres in G 2(R n), to appear in J. Reine Angew. Math.
A. Bahy-El-Dien and J. C. Wood, The explicit construction of all harmonic two-spheres in quaternionic projective space, preprint, Univ. of Leeds, 1989.
A. Borel, On the curvature tensor of the Hermitian symmetric manifolds, Ann. of Math. 71 (1960), 508–521.
A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces I, Amer. J. Math. 80 (1958), 458–538.
D. Burns, F. Burstall, P. de Bartolomeis and J. Rawnsley, Stability of harmonic maps of Kähler manifolds, J. Differential Geom. 30 (1989), 579–594.
D. Burns and P. de Bartolomeis, Applications harmoniques stables dans P n, Ann. Scient. Ec. Norm. Sup. 21 (1988), 159–177.
F. Burstall and J. Rawnsley, Spheres harmoniques dans les groupes de Lie compacts et curbes holomorphes dans les espaces homogenes, C. R. Acad. Sc. Paris 302 (1986), 709–712.
F. Burstall, J. Rawnsley and S. Salamon, Stable harmonic 2-spheres in symmetric spaces, Bull. Amer. Math. Soc. 16 (1987), 274–278.
F. Burstall and S. Salamon, Tournaments, flags and harmonic maps, Math. Ann. 277 (1987), 249–265.
F. Burstall and J. C. Wood, The construction of harmonic maps into complex Grassmannians, J. Differential Goem. 23 (1986), 255–297.
E. Calabi and E. Vesentini, On compact, locally symmetric Kähler manifolds, Ann. of Math. 71 (1960), 472–507.
B. Y. Chen and T. Nagano, Totally geodesic submanifolds of symmetric spces, II, Duke Math. J. 45 (1978), 405–425.
S. S. Chern and J. G. Wolfson, Harmonic maps of the 2-sphere into a complex Grassmann manifold, II, Ann. of Math. 125 (1987), 301–335.
J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc. 10 (1978), 1–68.
J. Eells and L. Lemaire, Another report on harmonic maps, Bull. London Math. Soc. 20 (1988), 385–524.
J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109–160.
J. Eells and J. C. Wood, Restrictions on harmonic maps of surfaces, Topology 15 (1976), 263–266.
J. Eells and J. C. Wood, Harmonic maps from surfaces to complex projective spaces, Adv. in Math. 49 (1983), 217–263.
D. S. Freed, Flag manifolds and infinite dimensional Kähler geometry, In “Infinite Dimensional Groups with Applications”, Math. Sci. Res. Inst. Publ. 4 (1985), 83–121, Springer-Verlag.
P. Griffiths and J. Harris, Principles of Algebraic Geometry, Pure and Applied Math., A Wiley-Interscience series, 1978.
M. A. Guest, Geometry of maps between generalized flag manifolds, J. Differential Geom. 25 (1987), 223–247.
N. J. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55 (1987), 59–126.
N. J. Hitchin, Harmonic maps from a 2-torus to the 3-sphere, a preprint.
R. Howard, The nonexistence of stable submanifolds, varifolds and harmonic maps in sufficiently pinched simply connected Riemannian manifolds, Mich. Math. J. 32 (1985), 321–334.
T. Ishihara, The Gauss map and non holomorphic harmonic maps, Proc. Amer. Math. Soc. 89 (1983), 661–665.
M. Itoh, On curvature properties of Kähler C-spaces, J. Math. Soc. Japan 30 (1978), 39–71.
M. Jaques and Y. Saint-Aubin, Infinite dimensional Lie algebras acting on the solution space of various σ-models, J. Math. Phys. 28 (1987), 2463–2479.
S. Kobayashi, Differential Geometry of Complex Vector Bundles, Publ. Math. Soc. Japan 15, Iwanami Shoten Publ. and Princeton Univ. Press, 1987.
J. L. Koszul and B. Malgrange, Sur certaines structures fibrees complexes, Arch. Math. 9 (1958), 102–109.
H. B. Lawson and J. Simons, On stable currents and their application to global problems in real and complex geometry, Ann. of Math. 98 (1973), 427–450.
A. Lichnerowicz, Applications harmoniques et varietes Kählerinnes, Symp. Math. III (Bologna 1970), 341–402.
M. Maruyama, Theorem of Grauert Mülich-Spindler, Math. Ann. 255 (1981), 317–333.
M. J. Micallef and J. D. Moore, Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two planes, Ann. of Math. 127 (1988), 199–227.
H. Naito, On the holomorphicity of pluriharmonic maps, “Geometry of Manifolds”, Proceedings of the 35th symposium on differential geometry, edited by K. Shiohama, Perspectives in Math. Vol. 8, 1989, 419–425.
H. Nakagawa and R. Takagi, On locally symmetric Kähler submanifolds in a complex projective space, J. Math. Soc. Japan 28 (1976), 638–667.
S. Nishikawa, Gauss map of Kähler immersions, Tohoku Math. J. 27 (1975), 453–460.
Y. Ohnita, On pluriharmonicity of stable harmonic maps, J. London Math. Soc. 35 (1987), 563–568.
Y. Ohnita, Homogeneous harmonic maps into complex projective spaces, to appear in Tokyo J. Math..
Y. Ohnita and S. Udagawa, Stable harmonic maps from Riemann surfaces to compact Hermitian symmetric spaces, Tokyo J. Math. 10 (1987), 385–390.
Y. Ohnita and S. Udagawa, Stability, complex-analyticity and constancy of pluriharmonic maps from compact Kähler manifolds, to appear in Math. Z.
Y. Ohnita and G. Valli, Pluriharmonic maps into compact Lie groups and factorization into unitons, to appear in Proc. London Math. Soc..
T. Okayasu, Pinching and nonexistence of stable harmonic maps, Tohoku Math. J. 40 (1988), 213–220.
K. Ono, On the holomorphicity of harmonic maps from compact Kähler manifolds to hyperbolic Riemann surfaces, Proc. Amer. Math. Soc. 102 (1988), 1071–1076.
A. Pressley and G. Segal, “Loop Groups”, Oxford mathematical monographs, Clarendon press, Oxford, 1986.
J. Ramanathan, Harmonic maps from S 2 to G 2,4, J. Differential Geom. 19 (1984), 207–219.
A. Ramanathan and S. Subramanian, Einstein-Hermitian connections on principal bundles and stability, J. Reine Angew. Math. 390 (1988), 21–31.
J. Rawnsley, f-structures, f-twistor and harmonic maps, Geom. Seminar “Luigi Bianchi” II (1984) Lecture Notes in Math. 1164, 85–159, Springer-Verlag, Berlin.
R. Remmert, Holomorphe und meromorphe Abbildungen Komplexer Raume, Math. Ann. 133 (1957), 328–370.
S. Salamon, Harmonic and holomorphic maps, Geom. Seminar “Luigi Bianchi”II (1984), Lecture Notes in Math. 1164, Springer-Verlag, Berlin.
J. H. Sampson, Applications of harmonic maps to Kähler geometry, Contemp. Math. 49 (1986), 125–134.
M. Sato, Soliton equations as dynamical systems on an infinite dimensional Grassmann manifold, RIMS kokyuroku 439 (1981), 30–46.
S. Shatz, The decomposition and specialization of algebraic families of vector bundles, Compositio Math. 35 (1977), 163–187.
C. T. Simpson, Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization, J. Amer. Math. Soc. 1 (1988), 867–918.
Y.-T. Siu, The complex analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds, Ann. of Math. 112 (1980), 73–111.
Y.-T. Siu, Curvature characterization of hyperquadrics, Duke Math. J. 47 (1980), 641–654.
Y.-T. Siu, Strong rigidity of compact quotients of exceptional bounded symmetric domains, Duke Math. J. 48 (1981), 857–871.
Y.-T. Siu, Complex-analyticity of harmonic maps, vanishing and Lefschetz Theorems, J. Differential Geom. 17 (1982), 55–138.
Y.-T. Siu and S.-T. Yau, Compact Kähler manifolds of positive bisectional curvature, Invent. Math. 59 (1980), 189–204.
R. Takagi and M. Takeuchi, Degree of symmetric Kählerian submanifolds of a complex projective space, Osaka J. Math. 14 (1977), 501–518.
K. Takasaki, A new approach to the Yang-Mills equations, Commun. Math. Phys. 94 (1984), 35–59.
M. Takeuchi, Totally complex submanifolds of quaternionic symmetric spaces, Japan J. Math. 12 (1986), 161–189.
K. Tsukada, Parallel submanifolds in a quaternionic projective space, Osaka J. Math. 22 (1985), 187–241.
S. Udagawa, Minimal immersions of Kähler manifolds into complex space forms, Tokyo J. Math. 10 (1987), 227–239.
S. Udagawa, Pluriharmonic maps and minimal immersions of Kähler manifolds, J. London Math. Soc. (2) 37 (1988), 375–384.
S. Udagawa, Holomorphicity of certain stable harmonic maps and minimal immersions, Proc. London Math. Soc. (3) 57 (1988), 577–598.
K. Uhlenbeck, Harmonic maps into Lie groups (Classical solutions of the chiral model), J. Differential Geom. 30 (1989), 1–50.
G. Valli, On the energy spectrum of harmonic 2-spheres in unitary groups, Topology 27 (1988), 129–136.
G. Valli, Some remarks on geodesics in gauge groups and harmonic maps, J. Geom. Phys. 4 (1987), 335–359.
G. Valli, Harmonic gauges on Riemann surfaces and stable bundles, Ann. Inst. H. Poincaré (analyse non-lineaire) 6 (1989) 233–245.
R. O. Wells, Differential Analysis on Complex Manifolds, Prentice-Hall, Englewood Cliffs, N. J., 1973.
J. G. Wolfson, Harmonic sequences and harmonic maps of surfaces into complex Grassmann manifolds, J. Differential Geom. 27 (1988), 161–178.
J. G. Wolfson, Harmonic maps of the two-sphere into the complex hyperquadric, J. Differential Geom. 24 (1986), 141–152.
J. C. Wood, The explicit construction and parametrization of all harmonic maps from the two-sphere to a complex Grassmannian, J. Reine Angew. Math. 386 (1988), 1–31.
J. C. Wood, Explicit construction and parametrization of harmonic two-spheres in the unitary group, Proc. London Math. Soc. (3) 58 (1989), 608–624.
S.-T. Yau, On Calabi's conjecture and some results in algebraic geometry, Proc. Nat. Acad. Sci. USA 74 (1977), 1798–1799.
V. E. Zakharov and A. V. Mikhailov, Relativistically invariant two dimensional models of field theory which are integrable by means of the inverse scattering problem method, Sov. Phys. J. E. T. P. 47 (1978), 1017–1027.
V. E. Zakharov and A. B. Shabat, Integration of non-linear equations of mathematical physics by the method of inverse scattering II, Transl. Funk. Anal. 13 (1979), 166–174.
J.-Q. Zhong, The degree of strong nondegeneracy of the bisectional curvature of exceptional bounded symmetric domains, Several Complex Variables, Proc. 1981 Hangzhou Conf., 1984, 127–139.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag
About this paper
Cite this paper
Ohnita, Y., Udagawa, S. (1991). Complex-analyticity of pluriharmonic maps and their constructions. In: Noguchi, J., Ohsawa, T. (eds) Prospects in Complex Geometry. Lecture Notes in Mathematics, vol 1468. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086201
Download citation
DOI: https://doi.org/10.1007/BFb0086201
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54053-3
Online ISBN: 978-3-540-47370-1
eBook Packages: Springer Book Archive