Extending Information Geometry: Quasi-Statistical Structures on Metallic-Like Pseudo-Riemannian Manifolds
Turkish Journal of Mathematics and Computer Science, cilt.18, sa.1, ss.248-266, 2026 (Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 18 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.47000/tjmcs.1789376
- Dergi Adı: Turkish Journal of Mathematics and Computer Science
- Derginin Tarandığı İndeksler: Scopus, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.248-266
- Anahtar Kelimeler: Codazzi coupleds, conjugate connections, Metallic-like Pseudo-Riemannian manifolds, quasi-statistical structures
- Atatürk Üniversitesi Adresli: Evet
Özet
In this paper, we investigate the conditions under which quasi-statistical structures can be realized on metallic-like pseudo-Riemannian manifolds. By combining the flexibility of quasi-statistical geometry with the algebraic richness of metallic-like structures, we provide a unified framework for analyzing compatibility conditions among metrics, conjugate connections and structure tensors. We demonstrate that distinct conjugate connections such as h,˜h, J and J∗−conjugates, may yield quasi-statistical manifolds under appropriate compatibility assumptions. In particular, we establish a number of geometric results under the assumptions of Codazzi coupling and d∇-closedness. The novelty of our approach lies in combining the framework of metallic-like manifolds with quasi-statistical structures in the presence of torsion, thereby extending existing results in the literature and opening new directions for further research. Finally, we also present a theorem concerning the Tachibana operator, which highlights additional structural properties of the manifolds under consideration.