All metrics have curvature tensors characterized by its invariants as a limit: the epsilon-property

作者：Hervik Sigbjorn^*

来源：Classical and Quantum Gravity, 2011, 28(15): 157001.

DOI：10.1088/0264-9381/28/15/157001

We prove a generalization of the epsilon-property, namely that for any dimension and signature, a metric which is not characterized by its polynomial scalar curvature invariants; there is a frame such that the components of the curvature tensors can be arbitrary close to a certain 'background'. This 'background' is defined by its curvature tensors: it is characterized by its curvature tensors and has the same polynomial curvature invariants as the original metric.

• 出版日期2011-8-7