TIMELIKE KILLING VECTOR FIELDS ON A TIMELIKE OR LIGHTLIKE COMPLETE LORENTZIAN MANIFOLD

摘要

In this article, we prove that there is no timelike Killing vector field K on a timelike or lightlike complete Lorentzian manifold of positive sectional curvature for timelike planes. These results, in addition to the known ones for the spacelike case, provide an obstruction to the existence of such a K under any type of causal completeness.