摘要
构造一类次黎曼流形(M,D,g)并计算出此类次黎曼流形的步数,这里M≡R^3=R_x^2×R_t是3维光滑流形,D是由切向量场Y_1,Y_2生成的2维光滑水平分布,其中Y_1=1/((1+|x|^(4k+2))^(1/2))(/(x_1)+2x_2|X|^(2k)/(t)),Y_2=1/((1+|x|^(4k+2))^(1/2)) (/(x_2)-2x_1|X|^(2k)/(t)),k≥0是整数,g是定义在D上的正定度量。
In this paper we give a certain sub-Riemannian manifold (M,D,g) and the step of it, where M≡R^3=Rx^2×Rt is a three dimentional smooth manifold, D is a two dimentional smooth horizontal distribution generated by vector fields Y1=1/√1+|x|^4k+2( /x1+2x2|x|^2k /t),Y2=1/√1+|x|^4k+2 ( / x2-2x1|x|^2k / t),k≥0 is an integer, and g is a positive definite metric defined on D.
出处
《黄山学院学报》
2008年第5期10-12,共3页
Journal of Huangshan University
关键词
次黎曼流形
水平分布
括号生成
步数
sub-Riemannian manifold
horizontal distribution
bracket-generating
step