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.
Weakly Z-symmetric manifolds / C.A. Mantica, L.G.A. Molinari. - In: ACTA MATHEMATICA HUNGARICA. - ISSN 0236-5294. - 135:1/2(2012), pp. 80-96.
Weakly Z-symmetric manifolds
C.A. Mantica;L.G.A. MolinariUltimo
2012
Abstract
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.File | Dimensione | Formato | |
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