Some properties of concircular, conharmonic and projective curvature tensors on 4-dimensional lorentzian and riemannian spaces

Abstract

We investigate some features of concircular, conharmonic, and projective curvature tensors on 4-dimensional Lorentzian and Riemannian spaces. Using the known holonomy algebras for the metric signatures (+, +, +, −) and (+, +, +, +), we prove some theorems on these tensor elds. In the case of spaces admitting parallel and recurrent vector elds, results are also obtained relating these tensor elds to suitable holonomy types. The eigenbivector structure of these tensor elds is also examined for both metric signatures. The interrelations between the Riemann curvature tensor and the investigated tensor elds are discussed, and some speci c examples are also presented.