关于曲面保持平均曲率不变的无穷小等距变形

关于曲面保持平均曲率不变的无穷小等距变形 ON THE SURFACE’S INFINTESIMAL I-ISOMETRIC DEFORMATIONS PRESERVING MEAN CURVATURE 李全英 Li Quanying 1 first-author Department of Mathematics Wuhan University Wuhan Hubei Department of Mathematics Wuhan University Wuhan Hubei Department of Mathematics, Wuhan University Department of Mathematics, Wuhan University 本文讨论欧氏空间E 3 中曲面M保持平均曲率H不变的Ⅰ-等距无穷小变形.得到了曲面M容许这种变形的一个充要条件为d·θ=0,其中θ为曲面M所确定的一个Ⅰ-形式（见定理1）,利用这个结果,得H=const的曲面容许这种变形（定理2）,这是O.Bonnet定理的推广.另外,还得到容许这种变形的曲面的几何性质（见定理3,4）.最后,讨论了一些特殊的曲面（如旋转曲面、可展曲面）,确定他们是否容许这种变形. In this paper, we Consider the infintesimal I-isometry deformations of surface M in E 3 , which preserve mean curvature H, We obtain a necessary and sufficient condition of surface M, which admit not-trivial infinitesimal this deformation: d*θ=0 （See Theorem 1）. using this result, we obtain again, surface M which H=constadmit this deformations （See Theorem 2）, and we get other spcial surfaces which admit this deformations （See theorems 3 and 4） 无穷小等距变形 平均曲率 高斯曲率 复结构 外微分 infinitesimal isometric deformation mean curvaturc Gauss curvature complex structure exterior differential 国家自然科学基金(61672102) 1988-02-01 2021-04-01 2