On Ricci Vector Fields and Almost Product Structures in Three-Dimensional Walker Manifolds
International Journal of Theoretical Physics, cilt.65, sa.9, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 65 Sayı: 9
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s10773-026-06445-8
- Dergi Adı: International Journal of Theoretical Physics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, INSPEC, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO), Technology Collection (ProQuest)
- Anahtar Kelimeler: Ricci vector fields, Walker manifolds, Strictly Walker manifolds, Product structure, Twin metric
- Atatürk Üniversitesi Adresli: Evet
Özet
Motivated by the vector fields φ(Ric) defined through the condition ∇φ=μRic, where μ is a real constant and φ denotes a vector field on the underlying manifold, this paper investigates the existence problem of Ricci vector fields (μ=1) on three-dimensional Lorentzian Walker manifolds (M3,gf). A theorem is established providing the necessary and sufficient conditions for their existence, followed by several propositions offering a local classification of the component functions of Ricci vector fields and of the functions f determining the Walker metric under specific geometric constraints. Further results characterize the existence of spacelike and timelike Ricci vector fields. Introducing a product structure J on the Walker manifold, we show that the metric gf is pure with respect to J, and we construct the associated twin metric Gf, whose index exhibits a particularly noteworthy behavior when f>0. Finally, a theorem is presented giving the necessary and sufficient conditions for the existence of Ricci vector fields with respect to the twin metric Gf on the almost product Walker manifold (M3,J,gf).