Weakly Z symmetric manifolds

Details Weakly Z symmetric manifolds Weakly Z symmetric manifolds

2011-02-25

arxiv.org/abs/1102.5240v1

Acta Math. Hungar. 135 (2012) 80 - 96

Mathematics

Differential Geometry

13 pages

Scientific paper

10.1007/s10474-011-0166-3

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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