Beltrami定理的推广

A GENERALIZATION OF THE BELTRAMI THEOREM

本文研究了Berwald流形之间的射影对应.利用Berwald流形上Weyl射影曲率张量的射影不变性,证明了当n>2时,与射影平坦的Berwald流形射影对应的黎曼流形Mn是常曲率流形,从而推广了Beltrami定理.

In the article, we study the projective maps between Berward manifolds. By using the projective invariant of Weyl projective curvature tensor, we prove that an n-dimensional Riemannian manifold which projectively corresponds to a projective flat Berwald manifold must have constant sectional curvature （n 〉 2）. Thus we generalize the Beltrami theorem.