کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1894654 | 1533740 | 2015 | 16 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: II-degenerate pseudo-Riemannian metrics II-degenerate pseudo-Riemannian metrics](/preview/png/1894654.png)
In this paper we study pseudo-Riemannian spaces with a degenerate curvature structure i.e. there exists a continuous family of metrics having identical polynomial curvature invariants. We approach this problem by utilising an idea coming from invariant theory. This involves the existence of a boost which is assumed to extend to a neighbourhood. This approach proves to be very fruitful: It produces a class of metrics containing all known examples of II-degenerate metrics. To date, only Kundt and Walker metrics have been given, however, our study gives a plethora of examples showing that II-degenerate metrics extend beyond the Kundt and Walker examples.The approach also gives a useful criterion for a metric to be II-degenerate. Specifically, we use this to study the subclass of VSI and CSI metrics (i.e., spaces where polynomial curvature invariants are all vanishing or constants, respectively).
Journal: Journal of Geometry and Physics - Volume 98, December 2015, Pages 384–399