Duality on Geodesics of Cartan Distributions and Sub-Riemannian Pseudo-Product Structures
Duality on Geodesics of Cartan Distributions and Sub-Riemannian Pseudo-Product Structures
复制标题
嘉当分布测地线与亚黎曼伪积结构的对偶性
DOI：
10.1515/dema-2015-0017
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发表时间：
2014
影响因子：
2
通讯作者：
Wataru Yukuno
中科院分区：
文献类型：
--
作者：
G. Ishikawa;Y. Kitagawa;Wataru Yukuno
给定一个具有Cartan分布的五维空间，异常测地线构成另一个具有锥形结构的五维空间。然后在(15)中证明，如果将锥形结构视为一个控制系统，则锥形结构的异常测地线空间自然地与原始空间相同。本文在更广泛的框架下，利用控制系统的商和次黎曼伪积结构，对反常测地线的对偶性进行了阐述。我们还考虑了锥体结构的可控性，描述了正常测地线和反常测地线上的约束哈密顿方程。
Abstract Given a five dimensional space endowed with a Cartan distribution, the abnormal geodesics form another five dimensional space with a cone structure. Then it is shown in (15), that, if the cone structure is regarded as a control system, then the space of abnormal geodesics of the cone structure is naturally identified with the original space. In this paper, we provide an exposition on the duality by abnormal geodesics in a wider framework, namely, in terms of quotients of control systems and sub-Riemannian pseudo-product structures. Also we consider the controllability of cone structures and describe the constrained Hamiltonian equations on normal and abnormal geodesics.
与亚布里曼结构相关的嘉当连接
DOI：
--
发表时间：
2008
期刊：
Differential Geometry and its Applications 26
影响因子：
--
作者：
W. Bauer;K. Furutani;Y. Agaoka;T. Morimoto
通讯作者：
T. Morimoto
影响因子：
1.9
作者：
Wensheng Liu;H. Sussman
通讯作者：
Wensheng Liu;H. Sussman