通过扭映射π:CP7→ HP3构造出HP3中10族共形极小曲面的例子.根据Eells和Wood在1983年得到的结论,水平调和映射在淹没映射下的像仍然是调和的.首先给出CP7中水平全纯曲面在局部下的一个分类定理.基于该分类定理以及Eells和Wood的结论,利用扭映射,构造出HP3中的共形极小曲面.
In this paper, we construct ten families of conformal minimal surfaces immersed into HP3 by the twistor map π:CP7→HP3. The construction is based on Eells and Wood's conclusion in 1983 that the projection of a horizontal harmonic map is also harmonic. Firstly, we give a characterization theorem for horizontal holomorphic surfaces in CP7. By this theorem and Eells and Wood's conclusion, we get some conformal minimal surfaces immersed into HP3 by the twisted map.
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