𝜁 (Ric)-vector fields on doubly warped product manifolds

Year 2023, Volume: 1 Issue: 2, 67 - 73, 17.12.2023

Sibel Gerdan Aydın , Moctar Traore , Hakan Mete Taştan

https://doi.org/10.26650/ijmath.2023.00008

Abstract

We investigate 𝜁 (Ric)-vector fields on doubly warped product manifolds. We obtain some results when the vector field is also 𝜁 (Ric) on factor manifolds.We prove that if a vector field is a 𝜁 (Ric)-vector field on a doubly warped product manifold, it is also a 𝜁 (Ric)-vector field on the factor manifolds under certain conditions. Also, we show that a vector field on a doubly warped product manifold can be a 𝜁 (Ric)-vector field with some conditions. Moreover we give two important applications of this concept in the Lorentzian settings, which are the doubly warped product generalized Robertson-Walker space-time and doubly warped product standard static space-time.

Keywords

𝜁(Ric)-vector field, warped product manifold, standard static space-times, generalized Robertson-Walker space-times

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