【摘要】 O．Bonnet首先研究了保持主曲率不变的曲面的等距变形问题[1]，并证明了常中曲率曲面具有保主曲率的等距变形1985年S．S．Chern证明了在欧氏空间中具有保持主曲率不变的非常中曲率曲面是W-曲面．[2]在此之后，陈秀雄等人对此作了进一步的讨论，得到了这样的W－曲面的Gauss曲率和中曲率所满足的微分方程[3]．本文讨论了三维常曲率空间中保持主曲率不变的曲面的等距问题，得到了具有这种等距变形的曲面的性质及曲面的Gauss曲率、中曲率所满足的微分方程，推广了文献[2]和[3]中的结果．更多还原

【Abstract】 The problem of isometric deformation of surface with constant principal curvatures was studied by O. Bonnet first. He proved that surface with constant mean curvature could preserve isometric deformation of principal curvatures. In 1985, S. S.Chern proved the non-constant mean curvature surface in R3 capable of preserving principal curvatures is W-surface. Chern Xiuxiong and Peng Chiakuei studied this problem further and obtained the equations for mean curvature and Gauss curvature of this Wsurface. In this paper, we discuss the isometric deformation of surface keeping principal curvatures unchanged in a 3-dimensional. constant curvature space, and obtain the properties of this surface and equations satisfied by the Gauss curvature and mean curvature of surface with this deformation.更多还原