设 G 是一个Carnot群,D={e1,e1}是G上一个左不变括号生成分布. 在本文中,构造存在一类维数大于5的Carnot群,其上存在严格非正态极值. 从而可知Golé,Karidi构造的第一个存在奇异测地线的Carnot群只是本文的一个特殊例子.
Abstract
Let G be a Carnot group and D={e1,e1} be a bracket generating left invariant distribution on G. In this paper, we can construct a class of n-dimensional (n > 5) Carnot groups such that there exist strictly abnormal extremals in it. So we know that the first Carnot group with singular geodesics which constructed by Golé, Karidi is only a particular example in present paper.
关键词
奇异测地线 /
严格非正态极值 /
Carnot群
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Key words
singular geodesic /
strictly abnormal extremal /
Carnot group
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参考文献
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