Harmonic maps on the tangent bundle according to the ciconia metric
Hacettepe Journal of Mathematics and Statistics, cilt.54, sa.1, ss.75-89, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 54 Sayı: 1
- Basım Tarihi: 2025
- Doi Numarası: 10.15672/hujms.1343052
- Dergi Adı: Hacettepe Journal of Mathematics and Statistics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
- Sayfa Sayıları: ss.75-89
- Anahtar Kelimeler: ciconia metric, harmonic maps, tangent bundle
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Atatürk Üniversitesi Adresli: Evet
Özet
The focus of this paper revolves around investigating the harmonicity aspects of various mappings. Firstly, we explore the harmonicity of the canonical projection π: (T M, ˜g) → (M2n, J, g), where (M2n, J, g) represents an anti-paraKähler manifold and (T M, ˜g) its tangent bundle with the ciconia metric. Additionally, we study the harmonicity of a vector field ξ, treated as mappings from M to T M. In this context, we consider the harmonicity relations between the ciconia metric ˜g and the Sasaki metricSg, examining their mutual interactions. Furthermore, we investigate the Schoutan-Van Kampen connection and the Vrãnceanu connection, both associated with the Levi-Civita connection of the ciconia metric. Our analysis also includes the computation of the mean connections for the Schoutan-Van Kampen and Vrãnceanu connections, thereby providing insights into their properties. Finally, our exploration( extends to the second fundamental form of the identity mapping from (T M, ˜g) to T M, ∇m) ( and T M,˜∇∗m). Here ∇m and˜∇∗m denote the mean connections associated with the Schoutan-Van Kampen and Vrãnceanu connections, respectively.