Harmonic maps into real hyperbolic space
Abstract
In [2,4,5,6,7 ] Calabi, Borbosa and Chern showed that there is a one-to-one correspondence between arbitrary pairs of full isotropic (terminology as in [8]) harmonic maps
from a Riemann surface to Euclidean sphere and full totally isotropic holomorphic maps
from the surface to complex projective space.In this paper we show, very explicity, how to construct a similar one-to-one correspondence when
is replaced by real hyperbolic space
with its standard metric. We get over a difficulty encountered by Barbosa of dealing with the zeros of certain wedge product by a technique adapted from [8].(The case of indefinite complex hyperbolic and projective spaces will be considered in a separate paper).
![\pm\phi:M→ S<sup>2m</sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/30cff51878d445c85d576253460a1fef.png)
![f:M→ℂP<sup>2m</sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/b0071415764e5c727a377e5047173eab.png)
![S<sup>2m</sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/7667d0d6b20e10c2cfeba0f3e4f6b123.png)
![H<sup>2m</sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/fc7a2fa5484e962e6bec1b44749356f7.png)
DOI Code:
10.1285/i15900932v3n1p29
Full Text: PDF