Exploring Conformal Soliton Structures in Tangent Bundles with Ricci-Quarter Symmetric Metric Connections

Li Y., GEZER A., Karakas E.

Mathematics, cilt.12, sa.13, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 13
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3390/math12132101
  • Dergi Adı: Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: complete lift metric, conformal Ricci soliton, conformal Yamabe soliton, gradient conformal Ricci soliton, gradient conformal Yamabe soliton, Ricci-quarter symmetric metric connection, tangent bundle
  • Atatürk Üniversitesi Adresli: Evet

Özet

In this study, we investigate the tangent bundle (Formula presented.) of an n-dimensional (pseudo-)Riemannian manifold M equipped with a Ricci-quarter symmetric metric connection (Formula presented.). Our primary goal is to establish the necessary and sufficient conditions for (Formula presented.) to exhibit characteristics of various solitons, specifically conformal Yamabe solitons, gradient conformal Yamabe solitons, conformal Ricci solitons, and gradient conformal Ricci solitons. We determine that for (Formula presented.) to be a conformal Yamabe soliton, the potential vector field must satisfy certain conditions when lifted vertically, horizontally, or completely from M to (Formula presented.), alongside specific constraints on the conformal factor (Formula presented.) and the geometric properties of M. For gradient conformal Yamabe solitons, the conditions involve (Formula presented.) and the Hessian of the potential function. Similarly, for (Formula presented.) to be a conformal Ricci soliton, we identify conditions involving the lift of the potential vector field, the value of (Formula presented.), and the curvature properties of M. For gradient conformal Ricci solitons, the criteria include the Hessian of the potential function and the Ricci curvature of M. These results enhance the understanding of the geometric properties of tangent bundles under Ricci-quarter symmetric metric connections and provide insights into their transition into various soliton states, contributing significantly to the field of differential geometry.