Carnot 群上严格非正态极值的存在性

黄体仁

数学学报 ›› 2014, Vol. 57 ›› Issue (4) : 745-750.

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数学学报 ›› 2014, Vol. 57 ›› Issue (4) : 745-750. DOI: 10.12386/A2014sxxb0069
论文

Carnot 群上严格非正态极值的存在性

    黄体仁1,2
作者信息 +

The Existence of Strictly Abnormal Extremals in Carnot Groups

    Ti Ren HUANG1,2
Author information +
文章历史 +

摘要

G 是一个Carnot群,D={e1e1}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={e1e1} 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

Key words

singular geodesic / strictly abnormal extremal / Carnot group

引用本文

导出引用
黄体仁. Carnot 群上严格非正态极值的存在性. 数学学报, 2014, 57(4): 745-750 https://doi.org/10.12386/A2014sxxb0069
Ti Ren HUANG. The Existence of Strictly Abnormal Extremals in Carnot Groups. Acta Mathematica Sinica, Chinese Series, 2014, 57(4): 745-750 https://doi.org/10.12386/A2014sxxb0069

参考文献

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基金

国家自然科学基金资助项目(10771102)

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