期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1979
卷号：76
期号：4
页码：1550-1553
DOI：10.1073/pnas.76.4.1550
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：It is shown that any weakly stable Yang-Mills field of type SU2 or SU3 on the four-sphere must be self-dual or anti-self-dual. Any Yang-Mills field on Sn, n [≥] 5, is unstable. Examples of stable fields on S4 and Sn/{Gamma} for n [≥] 5 and {Gamma} [!=] {e} are given. It is also shown that, for any Yang-Mills field R on S4, the pointwise condition ||R-|| 2 < 3 (or ||R+|| 2 < 3) implies that R- = 0 (or respectively that R+ = 0). In general, any Yang-Mills field R on Sn, n [≥] 3, that satisfies the pointwise condition ||R||2 < [1/2](2n) is trivial. If n = 3 or 4, the condition ||R||2 [≤] [1/2](2n) implies that either R is the trivial field or it is the direct sum of a trivial field with a field of tangent spinors carrying the standard connection.
