数学物理学报(英文版) ›› 1995, Vol. 15 ›› Issue (4): 415-421.

• Articles • 上一篇    下一篇

EXACT-VOLUME DIFFERENTIAL FORM DE RHAM COHOMOLOGY AND HAMILTON VARIATIONAL PRINCIPLE

王继春   

  1. Dept. Math. Phys. of Wuhan Unly. of Technology., Wuhan 430070, China
  • 收稿日期:1993-06-22 出版日期:1995-12-25 发布日期:1995-12-25

EXACT-VOLUME DIFFERENTIAL FORM DE RHAM COHOMOLOGY AND HAMILTON VARIATIONAL PRINCIPLE

Wang Jichun   

  1. Dept. Math. Phys. of Wuhan Unly. of Technology., Wuhan 430070, China
  • Received:1993-06-22 Online:1995-12-25 Published:1995-12-25

摘要: In this paper, we suggested exact-volume differential form (for short:EVDF) and proved four theorems correlative with them:1. existence theorem, 2. cohomology theorem,3. constant multiple theorem, and 4. equal gauge theorem. And their application were discussed also. For examlpe, we deduced the particle dynamic equation of the special theory of relativity. At the same time we analyzed and contrasted cohomology theory with Hamilton's variational principle. The contrast showed the superiority of cohomology theory. Moreover,we gave a more complete classification list of differential forms.

关键词: exact-volume differential form, cohomology

Abstract: In this paper, we suggested exact-volume differential form (for short:EVDF) and proved four theorems correlative with them:1. existence theorem, 2. cohomology theorem,3. constant multiple theorem, and 4. equal gauge theorem. And their application were discussed also. For examlpe, we deduced the particle dynamic equation of the special theory of relativity. At the same time we analyzed and contrasted cohomology theory with Hamilton's variational principle. The contrast showed the superiority of cohomology theory. Moreover,we gave a more complete classification list of differential forms.

Key words: exact-volume differential form, cohomology