|
|
| |
| The Improvement of the Kneser Theorem and Its Applications |
| |
Citation： |
Zhu Deming.The Improvement of the Kneser Theorem and Its Applications[J].Chinese Annals of Mathematics B,1987,8(3):364~374 |
| Page view： 1001
Net amount： 686 |
Authors： |
Zhu Deming; |
|
|
| Abstract： |
In this paper, first it is proved that on the Mobius strip M there is a unique periodic orbit of the continuous flow f which is the generator of the fundamental group \pi_1(M), where f is tangent (or transversal) to the boundary and has no fixed point on M. Then the results of the Kneser theorem are augmented. On the base of. these two results, the classification theorems for M and the Klein bottle are given, which are some more profound than those given in [1]. At last, applying the improved Kneser theorem to i some continuous flows on torus, the author gets the results that there exist periodic orbits the number of which is even (at least 2), and describes some qualitative behaviors of the orbits. Moreover, some simple applications to the general nonorientable 2-manifold, particularly to the,projective plane, are also mentioned. |
Keywords： |
|
Classification： |
|
|
|
Download PDF Full-Text
|
|
|
|
