曲面上测地线集合的测度与直线汇的Cartan测度

The measure for congruences of geodesics on surfaces and Cartan measure for congruences of lines

利用活动标架方法,获得了曲面上测地线集合的密度就是其切线汇的Cartan密度,因此在空间的运动群下保持不变,同时也用测地线集合的测度解释了法线汇的Cartan测度为零.

In light of moving frames , the density for congruences of geodesics on surfaces is equal to Cartan density for congruences of their tangents , therefore , keeps invariant under the groups of motions on spaces . At the same time , by the measure for congruences of geodesics , Cartan measure for one parameter congruences of normals is zero .