Investigation of some special tensor fields on space-times with holonomy algebras

Abstract

This paper studies the concircular, projective and conharmonic curvature tensors on $4-$dimensional Lorentzian manifolds known as space-times. We obtain some properties of these tensor fields by relating the known holonomy algebras for Lorentz signature $(+, +, +, -)$. For the space-times admitting special vector fields, such as parallel and recurrent vector fields, some theorems are proved. The eigenbivector structure of the investigated tensor fields is also examined in these spaces. These results obtained by considering the holonomy theory are associated with the algebraic classification of the Riemann curvature and Ricci tensors for Lorentz signature, and various examples related to the study are also given.