Let and be hyperkähler manifolds. We study stationary quaternionic maps between and . 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 . 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 in the hyperkähler surface studied by Atiyah-Hitchin.
@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}, pages = {375--388}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 4}, number = {3}, year = {2005}, zbl = {1170.53312}, mrnumber = {2185957}, language = {en}, url = {archive.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, 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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