2023/10/17 by Alekseevsky, Dmitri V., Ganji, Masoud, Schmalz, Gerd +1
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2310.10938
We explicitly derive the Christoffel symbols in terms of adapted frame fields for the Levi-Civita connection of a Lorentzian n-manifold (M, g), equipped with a prescribed optical geometry of Kähler-Sasaki type. The formulas found in this paper have several important applications, such as determining the geometric invariants of Lorentzian manifolds with prescribed optical geometries or solving curvature constraints.