Projective structure in 4-dimensional manifolds with positive definite metrics

JOURNAL OF GEOMETRY AND PHYSICS

卷:62

Article

Hall, Graham¹  Wang, Zhixiang¹ 

[1] Univ Aberdeen, Inst Math, Aberdeen AB24 3UE, Scotland

关键词: Projective;    Holonomy;    Geodesics;    Positive definite metric;   

DOI  :  10.1016/j.geomphys.2011.10.007

来源: Elsevier

【 摘 要 】

This paper considers the situation on a 4-dimensional manifold admitting two metric connections, one of which is compatible with a positive definite metric, and which have the same unparametrised geodesics. It shows how, in many cases, the relationship between these connections and metrics can be found. In many of these cases, the connections are found to be necessarily equal. The general technique used is that based on a certain classification of the curvature tensor together with holonomy theory. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free