平行映射下保测地线的曲面

摘要

By the classical theory of differential geometry, we get some local properties of surfaces which keep geodesics corresponding under parallel mapping. Moreover, we discuss the geodesic coordinates of these kind of surfaces and finally proved that only three kins of surfaces satisfy the precondition.%利用古典微分几何方法，讨论了在平行映射下测地线不变的曲面若干局部性质；研究了该类曲面的测地坐标系，并最终得出满足该条件的曲面只有三类。