Spaces of harmonic maps of the projective plane to the four-dimensional sphere

被引：1

作者：

Gabdurakhmanov, Ravil ^{[1
,2
,3
]}

机构：

[1] Natl Res Univ Higher Sch Econ, Fac Math, 6 Usacheva Str, Moscow 119048, Russia

[2] Independent Univ Moscow, Bolshoy Vlasyevskiy Pereulok 11, Moscow 119002, Russia

[3] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England

来源：

JOURNAL OF GEOMETRY | 2020年 / 111卷 / 03期

关键词：

Harmonic map; twistor lift; projective plane; LAPLACE-BELTRAMI OPERATOR; MINIMAL IMMERSIONS; ISOPERIMETRIC INEQUALITY; EIGENVALUE; 2-SPHERES; CONNECTEDNESS; S2;

D O I：

10.1007/s00022-020-00550-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The spaces of harmonic maps of the projective plane to the four-dimensional sphere are investigated in this paper by means of twistor lifts. It is shown that such spaces are empty in case of even harmonic degree. In case of harmonic degree less than 6 it was shown that such spaces are path-connected and an explicit parameterization of the canonical representatives was found. In addition, the last section provides comparisons with the known results for harmonic maps of the two-dimensional sphere to the four-dimensional sphere of harmonic degree less than 6.

引用

页数：23

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