Quaternionic maps and minimal surfaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 4 (2005) no. 3, p. 375-388

Let (M,J α ,α=1,2,3) and (N,𝒥 α ,α=1,2,3) be hyperkähler manifolds. We study stationary quaternionic maps between M and N. We first show that if there are no holomorphic 2-spheres in the target then any sequence of stationary quaternionic maps with bounded energy subconverges to a stationary quaternionic map strongly in W 1,2 (M,N). We then find that certain tangent maps of quaternionic maps give rise to an interesting minimal 2-sphere. At last we construct a stationary quaternionic map with a codimension-3 singular set by using the embedded minimal 𝕊 2 in the hyperkähler surface M ˜ 2 0 studied by Atiyah-Hitchin.

Classification:  53C26,  53C43,  58E12,  58E20
@article{ASNSP_2005_5_4_3_375_0,
     author = {Chen, Jingyi and Li, Jiayu},
     title = {Quaternionic maps and minimal surfaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 4},
     number = {3},
     year = {2005},
     pages = {375-388},
     zbl = {1170.53312},
     mrnumber = {2185957},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2005_5_4_3_375_0}
}
Chen, Jingyi; Li, Jiayu. Quaternionic maps and minimal surfaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 4 (2005) no. 3, pp. 375-388. http://www.numdam.org/item/ASNSP_2005_5_4_3_375_0/

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