Harmonic tori and generalised Jacobi varieties

TY - JOUR

T1 - Harmonic tori and generalised Jacobi varieties

AU - McIntosh, I.

PY - 2001/4

Y1 - 2001/4

N2 - This article shows that every non-isotropic harmonic 2-torus in complex projective space factors through a generalised Jacobi variety related to the spectral curve. Each map is composed of a homomorphism into the variety and a rational map off it. The same ideas allow one to construct (pluri)-harmonic maps of finite type from Euclidean space into Grassmannians and the projective unitary groups. Further, some of these maps will be purely algebraic. For maps into complex projective space the algebraic maps of the plane are always doubly periodic i.e. they yield 2-tori. The classification of all these algebraic maps remains open.

AB - This article shows that every non-isotropic harmonic 2-torus in complex projective space factors through a generalised Jacobi variety related to the spectral curve. Each map is composed of a homomorphism into the variety and a rational map off it. The same ideas allow one to construct (pluri)-harmonic maps of finite type from Euclidean space into Grassmannians and the projective unitary groups. Further, some of these maps will be purely algebraic. For maps into complex projective space the algebraic maps of the plane are always doubly periodic i.e. they yield 2-tori. The classification of all these algebraic maps remains open.

M3 - Article

SN - 1019-8385

VL - 9

SP - 423

EP - 449

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

IS - 2

ER -