Local normal forms for geodesically equivalent pseudo-Riemannian metrics
Differential Geometry
2017-11-30 v2 General Relativity and Quantum Cosmology
Analysis of PDEs
Abstract
Two pseudo-Riemannian metrics and are geodesically equivalent, if they share the same (unparameterized) geodesics. We give a complete local description of such metrics which solves the natural generalisation of Beltrami problem for pseudo-Riemannian metrics.
Keywords
Cite
@article{arxiv.1301.2492,
title = {Local normal forms for geodesically equivalent pseudo-Riemannian metrics},
author = {Alexey V. Bolsinov and Vladimir S. Matveev},
journal= {arXiv preprint arXiv:1301.2492},
year = {2017}
}
Comments
this is an extended version of the submitted paper. It contains all proofs with all details and also an appendix where we explain how can one construct a complex structure by a (1,1)-tensor such that all its eigenvalues are not real and such that the Nijenhuis torsion vanishes