华东师范大学学报(自然科学版) ›› 2007, Vol. 2007 ›› Issue (3): 16-22.

• 数学 统计学 • 上一篇    下一篇

R3的射丛上Gauss方程不变解

何梅1,2   

  1. 1. 淮阴师范学院 数学系, 江苏 淮安 223001; 2. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2006-05-22 修回日期:2006-10-11 出版日期:2007-05-25 发布日期:2007-05-25
  • 通讯作者: 何梅

Invariant Solutions of Gauss Equation on Jet Bundle R3(Chinese)

HE Mei1,2   

  1. 1. Department of Mathematics, Huaiyin Teachers College, Huaian Jiangsu 223001, China; 2. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2006-05-22 Revised:2006-10-11 Online:2007-05-25 Published:2007-05-25
  • Contact: HE Mei

摘要： 用对称群的方法研究了在R3的射丛上Gauss 曲率方程所容许的不变群及群不变解, 并得到相应的不变群及一些群不变解. 同时, 从方程的角度得到了具常Gauss曲率曲面的一些结果.

关键词: 不变曲面, 不变群, 群不变解, 延拓, 射流空间, 不变曲面, 不变群, 群不变解, 延拓, 射流空间

Abstract: Using symmetry group methods, this paper studied the invariant groups admitted by Gauss curvature equation on jet bundle R3. Invariant groups, infinitesimal generators of the corresponding invariant groups and some group-invariant solutions were found. Results about some surfaces which have constant Gauss curvature were given.

Key words: invariant groups, group-invariant solutions, prolongation, jet space, invariant surface, invariant groups, group-invariant solutions, prolongation, jet space

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