ζ (Ric)-Vector Fields and Ricci Solitons

Tastan H. M., Traore M., Gerdan Aydin S.

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1556/012.2026.04352
  • Dergi Adı: STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO)
  • İstanbul Üniversitesi Adresli: Evet

Özet

We prove that any zeta (Ric)-vector field is closed on a Riemannian manifold and obtain some new characterizations for Riemannian manifolds admitting zeta (Ric)-vector fields. The cases of compactness and orientability are also considered. Then, we study the rigidity of Ricci solitons whose potential vector fields are zeta (Ric). In particular, we prove that the potential vector fields of steady gradient Ricci solitons are always zeta (Ric). We present several illustrative examples to support our findings. Finally, we establish Ricci solitons on submanifolds equipped with zeta (Ric)-vector fields.