Notes on a conformal characterization of $2$-dimensional Lorentzian manifolds with constant Ricci scalar curvature

Nicolò Cangiotti; Mattia Sensi

Notes on a conformal characterization of $2$-dimensional Lorentzian manifolds with constant Ricci scalar curvature

Mathematical Physics 2020-05-19 v1 math.MP

Authors: Nicolò Cangiotti , Mattia Sensi

Abstract

We present a characterization of $2$ -dimensional Lorentzian manifolds with constant Ricci scalar curvature. It is well known that every $2$ -dimensional Lorentzian manifolds is conformally flat, so we rewrite the Ricci scalar curvature in terms of the conformal factor and we study the solutions of the corresponding differential equations. Several remarkable examples are provided.

Keywords

lorentzian manifolds constant ricci scalar curvature conformal characterization conformally flat differential equations

Cite

@article{arxiv.2005.08671,
  title  = {Notes on a conformal characterization of $2$-dimensional Lorentzian manifolds with constant Ricci scalar curvature},
  author = {Nicolò Cangiotti and Mattia Sensi},
  journal= {arXiv preprint arXiv:2005.08671},
  year   = {2020}
}

Comments

8 pages, 5 figures

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