4步次洛仑兹流形上的测地线（英文）  

Geodesics in a Step 4 Sub-Lorentzian Manifold

作　　者：黄体仁 孙明保[2] 谭沈阳[3] HUANG Tiren;SUN Mingbao;TAN Shenyang(Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, 310018, P. R. China;School of Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan, 314006, P. R. China;Taizhou Institute of Science and Technology, Nanjing University of Science and Technology, Taizhou, Jiangsu, 225300, P. R. China)

机构地区：[1]浙江理工大学数学系 [2]湖南理工学院数学学院 [3]南京理工大学泰州科技学院

出　　处：《数学进展》2018年第4期580-594,共15页Advances in Mathematics（China）

基　　金：Supported by NSFC(Nos.11401531,11271118);the Natural Science Foundation of Jiangsu Province(No.BK20140965);the Natural Science Foundation of Zhejiang Province(No.LQ17A010010)

摘　　要：设(R^3,D,g)是一个次洛仑兹流形,其中D是一个4步括号生成分布,g是定义在D上的次洛仑兹度量,它是一个惯性指数为1的度量.本文首先计算了类时将来方向曲线的可达集,其次,给出了正规测地线的完全描述并计算了连接原点与任意点的正规测地线的条数.最后,证明了类时测地线不存在共轭点.Let （R^3, D, g） be a sub-Lorentzian manifold, where D is a 4-step bracket gen- erating distribution and g is a sub-Lorentzian metric which is a nondegenerate metric of index 1. This paper computes reachable sets by time-like future directed curves. Second, we give a complete description of the normal geodesics and characterize numbers of normal geodesics between the origin and any other points. Third, we prove that there are no conjugate points of timelike geodesics.

关 键 词：次洛仑兹流形 可达集 正规测地线 

分 类 号：O189.31[理学—数学]