Acta Mathematica Hungarica

, Volume 135, Issue 1–2, pp 80–96 | Cite as

Weakly Z-symmetric manifolds

  • Carlo Alberto Mantica
  • Luca Guido MolinariEmail author


We introduce a new kind of Riemannian manifold that includes weakly-, pseudo- and pseudo projective Ricci symmetric manifolds. The manifold is defined through a generalization of the so called Z tensor; it is named weakly Z-symmetric and is denoted by (WZS) n . If the Z tensor is singular we give conditions for the existence of a proper concircular vector. For non singular Z tensors, we study the closedness property of the associated covectors and give sufficient conditions for the existence of a proper concircular vector in the conformally harmonic case, and the general form of the Ricci tensor. For conformally flat (WZS) n manifolds, we derive the local form of the metric tensor.

Key words and phrases

weakly-Ricci symmetric manifold pseudo- projective Ricci symmetric conformal curvature tensor quasi conformal curvature tensor conformally symmetric conformally recurrent Riemannian manifolds weakly Z-symmetric manifold 

2010 Mathematics Subject Classification

53B20 53B21 


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  1. 1.Physics DepartmentUniversità degli Studi di Milano and I.N.F.N.MilanoItaly

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