Geodesic
A Space of Harmonic Maps from a Sphere into the Complex Projective Space
Canadian journal of mathematics, Tome 65 (2013) no. 4, pp. 879-904

Voir la notice de l'article provenant de la source Cambridge University Press

Guest–Ohnita and Crawford have shown the path-connectedness of the space of harmonic maps from ${{S}^{2}}$ to $\text{C}{{P}^{n}}$ of a fixed degree and energy. It is well known that the $\partial$ transform is defined on this space. In this paper, we will show that the space is decomposed into mutually disjoint connected subspaces on which $\partial$ is homeomorphic.
DOI : 10.4153/CJM-2012-052-6
Mots-clés : 58E20, 58D15, harmonic maps, harmonic sequences, gluing 
Kawabe, Hiroko. A Space of Harmonic Maps from a Sphere into the Complex Projective Space. Canadian journal of mathematics, Tome 65 (2013) no. 4, pp. 879-904. doi: 10.4153/CJM-2012-052-6
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[CW] [CW] Chern, S. S. and G.Wolfson, J., Harmonic maps of the two-sphere into a complex Grassmann manifold II*. Ann. of Math. 125(1987), no. 2, 301–335. Google Scholar | DOI

[C] [C] Crawford, T. A., The space of harmonic maps from the 2-sphere to the complex projective plane. Canad. Math. Bull. 40(1997), no. 3, 285–295. Google Scholar | DOI

[EW] [EW] Eells, J. and Wood, J. C., Harmonic maps from surfaces to complex projective spaces. Adv. in Math. 49(1983), no. 3, 217–263. Google Scholar | DOI

[GH] [GH] Griffiths, P. and Harris, J., Principles of algebraic geometry. Pure and Applied Mathematics, Wiley-Interscience, New York, 1978. Google Scholar

[GO] [GO] Guest, M. A. and Ohnita, Y., Group actions and deformations for harmonic maps. J. Math. Soc. Japan 45(1993), no. 4, 671–704. Google Scholar | DOI

[K] [K] Kawabe, H., Harmonic maps from the Riemann sphere into the complex projective space and the harmonic sequences. Kodai Math. J. 33(2010), no. 3, 367–382. Google Scholar | DOI

[KN] [KN] Kobayashi, S. and Nomizu, K., Foundations of differential geometry. Vol. I and Vol. II, JohnWiley & Sons, Inc., New York, 1996. Google Scholar

[LW1] [LW1] Lemaire, L. and C.Wood, J., On the space of harmonic 2-spheres in CP2. Internat. J. Math. 7(1996), no. 2, 211–225. Google Scholar | DOI

[LW2] [LW2] Lemaire, L., Jacobi fields along harmonic 2-spheres in CP2 are integrable. J. London Math. Soc. (2) 66(2002), no. 2, 468–486. Google Scholar | DOI

[P] [P] Parker, T. H., Bubble tree convergence for harmonic maps. J. Differential Geom. 44(1996), no. 3, 595–633. Google Scholar

[PW] [PW] Parker, T. H. and G.Wolfson, J., Pseudoholomorphic maps and bubble trees. J. Geom. Anal. 3(1993), no. 1, 63–98. Google Scholar | DOI

[W] [W] G.Wolfson, J., Harmonic sequences and harmonic maps of surfaces into complex Grassmann manifolds. J. Differential Geom. 27(1988), no. 1, 161–178. Google Scholar

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