仿射联络空间切丛之间的映射─—纪念导师吴光磊教授

The Maps Between Manifolds with Linear Connections──to the Memory of Professor Wu Guanglei

本文依据Ｄｏｍｂｒｏｗｓｋｉ在仿射联络空间切丛上引进的近复结构，证明了：两个仿射联络空间之间的光滑映射的切映射保持近复结构不变的充分必要条件是该映射为全测地映射．

Based on Dombrowski′s construction of almost complex structre on the tangent bundle of a manifold with linear connection,it is proved that a map bet-ween two manifolds with linear connections is totally geodesic if and only if its tan-gential map between their tangent bundles preserves the almost complex structures.