Uniqueness of static decompositions

作者：Gutierrez Manuel^*; Olea Benjamin

来源：Annals of Global Analysis and Geometry, 2011, 39(1): 13-26.

DOI：10.1007/s10455-010-9222-4

• Static space
• Static vector field
• Isometric decomposition
• Lightlike sectional curvature

We classify static manifolds which admit more than one static decomposition whenever a condition on the curvature is fulfilled. For this, we take a standard static vector field and analyze its associated one parameter family of projections onto the base. We show that the base itself is a static manifold and the warping function satisfies severe restrictions, leading us to our classification results. Moreover, we show that certain condition on the lightlike sectional curvature ensures the uniqueness of static decomposition for Lorentzian manifolds.

• 出版日期2011-1