【摘要】 本文在一种特殊的三维半氏欧空间R_v~3中定义了复微分算子和广义高斯映射。在[1]的基础上进一步把广义Weierstrass公式推广到R_v~3中。通过这个公式,只要给定二维流形M上的非零C~1级函数H以及M上的光滑映射ψ,就可以构造出R_v~3中的曲面,使得H为它的平均曲率且ψ是它的高斯映射。更多还原

【Abstract】 In this paper, we develop the reults of the reference [1] and obtain thegeneralized weterstrass formula in an semi Euclidean space R_?~8. By this fo-rmula, if a C~1-class non-vanishing function H and a smooth map Ψ aregiven in a 2-dimensional manifold, we can build an immersed surface inR_o~3 such that H is the mean curvature. and Ψ is the Gauss mapping ofthis surface.更多还原