Quaternionic maps and minimal surfaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 3, pp. 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
Chen, Jingyi 1 ; Li, Jiayu 2

1 Department of Mathematics The University of British Columbia Vancouver, BC, Canada V6T 1Z2
2 Math. Group The abdus salam ICTP Trieste 34100 Italy and Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Beijing 100080, P. R. of China
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Chen, Jingyi; Li, Jiayu. Quaternionic maps and minimal surfaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 3, pp. 375-388. http://archive.numdam.org/item/ASNSP_2005_5_4_3_375_0/

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