关于调和映射和全测地映射的一个注记

A REMARK ON HARMONIC MAPS AND TOTALLY GEODESIC MAPS

本文考虑局部对称的共形平坦黎曼流形,推广了文[1]关于调和映射和全测地映射的一个结论。

In the present note we prove the following: Theorem Let f:M^n→M^m be a harmonic and relative affine mapping between Riemannian manifolds, M^m be a locally symetric and conformally flat Riemannian manifold, and M^n be a compact Riemannian manifold with positive Ricci curvatures.If each sectional carvature of M^n is not less than ?e( f ) K where K is the maximum of the sectional curvatures of M^m, and e ( f ) is the energy density of f, then f is a totally geodesic map.