On conformal invariance of isotropic geodesics

TL;DR

This paper explores the properties of isotropic geodesics within pseudoconformal manifolds, focusing on their applications to lightlike hypersurfaces, Lorentzian conformal structures, and Einstein space classification.

Contribution

It introduces new insights into the conformal invariance of isotropic geodesics and their role in the geometry of Lorentzian manifolds and Einstein spaces.

Findings

Characterization of isotropic geodesics in pseudoconformal manifolds

Applications to lightlike hypersurface geometry

Classification results for Einstein spaces

Abstract

We consider real isotropic geodesics on manifolds endowed with a pseudoconformal structure and their applications to the theory of lightlike hypersurfaces on such manifolds, the geometry of four-dimensional conformal structures of Lorentzian type, and a classification of the Einstein spaces.