A Unified Framework for Hermitian-Like and Anti-Hermitian-Like Geometries
Mediterranean Journal of Mathematics, cilt.23, sa.4, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 23 Sayı: 4
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s00009-026-03140-0
- Dergi Adı: Mediterranean Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Almost Hermitian-like manifolds, almost anti-Hermitian-like manifolds, Codazzi-coupled, anti-K & auml;hler manifolds, Hsu-type manifolds
- Atatürk Üniversitesi Adresli: Evet
Özet
This paper explores how certain generalized structures in differential geometry can be used to construct Kähler and anti-Kähler manifolds. In Hermitian-like settings, a specific type of tensor is introduced, and its antisymmetric component leads to the formation of Kähler-like geometries. In anti-Hermitian-like settings, the symmetric component of the similar tensor gives rise to anti-Kähler structures. The study consists of two main parts. The first part investigates almost Hermitian-like manifolds, where certain conditions such as the parallelism of a structural endomorphism and the vanishing of associated tensors help to characterize extended forms of Kähler geometry, including Hsu–Hermitian and Hsu–Kähler structures. The second part focuses on almost anti-Hermitian-like manifolds and demonstrates that, under appropriate compatibility with torsion-free connections, the geometry supports anti-Kähler and Hsu-B structures. These results together present a unified and systematic approach to generalizing classical complex geometric frameworks using differential and algebraic methods.