Proceedings of the American Mathematical Society

Author(s): Motoko Kotani
Journal: Proc. Amer. Math. Soc. 125 (1997), 2083-2092.
MSC (1991): Primary 49F10; Secondary 58E20
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Abstract: In the present paper, deformations of harmonic 2-spheres in the unit $n$

-sphere $S^{n}$ respecting the degree are studied. The limit maps of such deformations are characterized as harmonic maps with extra eigenfunctions. The space $Harm_{d}(S^{2},S^{n})$ of harmonic 2-spheres in $S^{n}$ with fixed degree $d$

is described in terms of such deformations and the limit maps.

[B]: J.L.M.Barbosa, On minimal immersions of $S^{2}$ into $S^{2m}(1)$ , Trans.Amer.Math.Soc. 210 (1975), 75-105. MR 51:11362
[BW1]: J.Bolton and L.M.Woodward, Moduli spaces of harmonic 2-spheres, Geometry and Topology of Submanifolds IV, World Scientific, 1992, pp. 143-151. MR 93g:58035
[BW2]: J.Bolton and L.M.Woodward, The space of harmonic maps of $S^{2}$ into $S^{n}$ , Geometry and Global Analysis, Report of the first MSJ International Research Institute, Tôhoku University, 1993, pp. 165-173. MR 96k:58053
[Ca]: E. Calabi, Minimal immersions of surfaces in Euclidean spheres, J. Diff. Geom. 1 (1976), 111-125. MR 38:1616
[Cr]: T.A.Crawford, The space of harmonic maps from the 2-spheres to complex projective space, preprint, McGill University., 1993.
[E1]: N.Ejiri, Minimal deformation of a nonfull minimal surface in $S^{4}(1)$ , Compositio.Math. 90 (1994), 183-209. MR 95a:53098
[E2]: N.Ejiri, The boundary of the space of full harmonic maps of $S^{2}$ into $S^{2m}(1)$ and extra eigenfunctions, in preparation.
[EK1]: N.Ejiri and M.Kotani, Index and flat ends of minimal surfaces, Tokyo J. Math. 16 (1993), 37-48. MR 94g:53003
[EK2]: N.Ejiri and M.Kotani, Minimal surfaces in $S^{2m}(1)$ with extra eigenfunctions, Quart. J. Math. 43 (1992), 421-440. MR 93k:53061
[FGKO]: M.Furuta, M.A.Guest , M.Kotani and Y.Ohnita, On the fundamental group of the space of harmonic 2-spheres in the n-sphere, Math. Z. 215 (1994), 503-518. MR 95e:58047
[GMO]: M.A.Guest, M.Mukai and Y.Ohnita, On the topology of spaces of harmonic 2-spheres in symmetric spaces, in preparation.
[GO]: M.A.Guest and Y.Ohnita, Group actions and deformation for harmonic maps, J. Math. Soc. Japan 45 (1993), 671-704. MR 94m:58058
[K]: M.Kotani, Connectedness of the space of minimal 2-spheres in $S^{2m}(1)$ , Proc. Amer. Math. Soc. 120 (1994), 803-810. MR 94e:58033
[L]: B.Loo, The space of harmonic maps of $S^{2}$ into $S^{4}$ , Trans. Amer. Math. Soc. 313 (1989), 81-103. MR 90k:58050
[M1]: M.Mukai, On connectedness of the space of harmonic 2-spheres in quaternionic projective spaces, to appear, Tokyo J.Math..
[M2]: M.Mukai, On connectedness of the space of harmonic 2-spheres in real Grassmann manifolds of 2-planes, Natur.Sci.Reo.Ochanomizu Univ. 44 (1993), 99-115. MR 95a:58031
[V]: J.L.Verdier, Two dimensional $\sigma$ models and harmonic maps from $S^{2}$ to $S^{2n}$ , Lecture Notes in Physics, vol. 180, Berlin, Springer, 1983, p. 136-141.

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