English

Bianchi type II,III and V diagonal Einstein metrics re-visited

Mathematical Physics 2015-05-18 v1 General Relativity and Quantum Cosmology math.MP Exactly Solvable and Integrable Systems

Abstract

We present, for both minkowskian and euclidean signatures, short derivations of the diagonal Einstein metrics for Bianchi type II, III and V. For the first two cases we show the integrability of the geodesic flow while for the third case a somewhat unusual bifurcation phenomenon takes place: for minkowskian signature elliptic functions are essential in the metric while for euclidean signature only elementary functions appear.

Keywords

Cite

@article{arxiv.1002.1454,
  title  = {Bianchi type II,III and V diagonal Einstein metrics re-visited},
  author = {Galliano Valent},
  journal= {arXiv preprint arXiv:1002.1454},
  year   = {2015}
}