黎曼G-流形上的基本向量场与测地线

FUNDAMENTAL VECTOR FIELDS AND GEODESICS IN RIEMANIAN G-MANIFOLDS

讨论了黎曼G 流形上一条曲线为测地线的充分条件 .证明了En 在李群G的等距作用下 ,对于一条不位于轨道上的曲线 ,若存在一个基本向量场在它上面的投影为非零常数 。

A sufficient condition for a curve being geodesic in Riemanian G manifolds is given.When the action of Lie groups G on E n is isometric, the author also obtains the fact that a curve is a line if the projectioin of a fundamental vector field to this curve which does not belong to an orbit is a nonzero constant.