Akademik Veri Yönetim Sistemi
Hacettepe Journal of Mathematics and Statistics, cilt.54, sa.1, ss.75-89, 2025 (SCI-Expanded)
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.