R^(2+p)中浸入曲面的共形G形变

Conformal Deformations of Surfaces in K^(2+p) Preserving the Gauss Map

对于Riemann曲面M到欧氏空间R+p的共形浸入f,本文引入了其伴随形式的概念;利用伴随形式和法丛的联络,我们建立了f是Gj-可形变的充分必要条件.主要结论如下:(1)如果f是G*-可形变的,则f具有平坦的法丛和闭的伴随形式;(2)当M是单连通时,如果f具有平坦的法丛和闭的伴随形式,则f是G*-可形变的.

In this article, we shall give the necessary and suffcient conditions for a conformally immersed surface f : M →R2+p to be G*-deformable. After introducing the concept of adjoint form for /, the following results are proved: (1) If / is G*-deformable, then the normal bundle of / is flat and the adjoint form is closed; (2) When M is simply connected, then / is G*-deformable if it has flat normal bundle and closed adjoint form.