Weakly Z-symmetric manifolds

By C. Mantica, L. Molinari. 2011

104 citations recorded by the source corpus.

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 weaklyZ-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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/89d455f07847716bed0b0325f239683b2bb363b8

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In Applied Mathematics

1. Absos Ali Shaikh
2. H. Kundu
3. C. Mantica
4. L. Molinari

In Astronomy and Astrophysics

1. Absos Ali Shaikh
2. H. Kundu
3. C. Mantica
4. L. Molinari

In Statistical and Nonlinear Physics

1. C. Mantica
2. L. Molinari

Citations in the corpus

• Generalized Robertson-Walker spacetimes — A survey (2016, background): “The result was extended by Mantica and Suh to pseudo-Z-symmetric spacetimes [63] and to weakly Z-symmetric spaces [61].”
• On pseudosymmetric manifolds (2014, background): “6)) with Z = S+ag, a being an arbitrary scalar function, was investigated in [33] (resp.”