The Levi-Civita connections of Lorentzian manifolds with prescribed optical geometries

Abstract

<p>We explicitly derive the Christoffel symbols in terms of adapted frame fields for the Levi-Civita connection of a Lorentziann-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 con-straints.</p>