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arXiv · 1102.5240

Weakly Z symmetric manifolds

Carlo A. Mantica·Luca G. Molinari
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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 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 tensor, 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.

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Carlo A. Mantica, Luca G. Molinari. 2011-02-25. Weakly Z symmetric manifolds. https://doi.org/10.1007/s10474-011-0166-3

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