Some Results on Immersions of Dold Manifolds  

关于Dold流形的浸入的某些结果

作　　者：王中良[1] 

机构地区：[1]北京工业大学应用数学系

出　　处：《Chinese Quarterly Journal of Mathematics》1991年第2期70-73,共4页数学季刊（英文版）

摘　　要：In this paper, we prove two theorema on immersions of Dold manifolds P(m, n). Let A_1={(2~s,0): s≥1};A_2={(0,2~s): s≥1}; A_3={(2~s,2~t):0≤s≤t};A_4={(2~s-1, 1): s=1}; A_5={(m,2~t): 2^(t+1)≤m, (2m+2^(t+1)-1)≡1 mod2}. We heve Theorem 1 Nonorientable P(m, n) immerses in R^(2m+4n-2) iff (m, n)(?)A_1. Theorem 2 (ⅰ) If (m, n)=(4s+2, 2t), s>0, then P (m, n) immerses in R^(2m+4n-3) iff (m, n)(?)A_3∪A^5. (ⅱ) If (m, u)=(4s, 2t), then P (m, n) immerses in R^(2m+4n-3) iff s>0 anb (m, n) A_1∪A_3∪A_5, or s=0 anb a(t)>2. (ⅲ) If (m, n)=4s+1, 2t), then P(m, n) immerses in R^(2m+4n-3) iff(m, n)A_3∪A_5; if (m, n)=(4s+3, 2t+1), then P(m, n) immerses in R^(2m+4n-3) iff (m, n)A_4. Theorem 2 (ⅲ) corrects an error in the paper [1] of Ucci concerning the case(m, n)=(4s+1, 2t).

关 键 词：DOLD流形 浸入 欧氏空间 

分 类 号：O189.3[理学—数学]