The Application of A New Type of Connection on $3$-dimensional Quasi-Sasakian Manifolds

Yıl 2025, Cilt: 10 Sayı: 2, 71 - 96, 30.08.2025

Azime Çetinkaya

https://doi.org/10.30931/jetas.1699264

Öz

Firstly we define a new type of quarter symmetric non-metric connection on almost
contact metric manifolds. Using this connection, we investigate some
curvature conditions on $3$-dimensional quasi-Sasakian manifolds e.g. $(\widetilde{R}(X,\xi).\widetilde{R})(Y,V)W=0$, $(\widetilde{P}(X,\xi).\widetilde{H})(Y,V)W=0$, $(\widetilde{R}(X,\xi).\widetilde{S})(Y,Z)=0,$ $(\widetilde{H}(X,\xi).\widetilde{S})(Y,Z)=0,$ and $(\widetilde{P}(X,\xi).\widetilde{S})(Y,Z)=0$. Also we study $\eta $-parallel $3$-dimensional quasi-Sasakian manifolds respect to this connection. Finally we give an example about 3-dimensional quasi-Sasakian manifold given with this connection.

Anahtar Kelimeler

Quarter-Symmetric Non-Metric Connection , 3-dimensional quasi-Sasakian manifolds , $\eta $-parallel.

3-boyutlu Quasi-Sasakian Manifoldlarda Tanımlanan Yeni Bir Koneksiyonun Uygulaması

Öz

Öncelikle, hemen hemen değme metrik manifoldlar üzerinde yeni bir çeyrek simetrik metrik olmayan koneksiyon tanımlayacağız. Bu koneksiyonu kullanarak, 3 boyutlu Quasi-Sasakian manifoldlar üzerinde $(\widetilde{R}(X,\xi).\widetilde{R})(Y,V)W=0$, $(\widetilde{P}(X,\xi).\widetilde{H})(Y,V)W=0$, $(\widetilde{R}(X,\xi).\widetilde{S})(Y,Z)=0,$ $(\widetilde{H}(X,\xi).\widetilde{S})(Y,Z)=0,$ ve $(\widetilde{P}(X,\xi).\widetilde{S})(Y,Z)=0$ gibi bazı eğrilik koşullarını araştıracağız. Ayrıca bu koneksiyona göre $\eta $-paralel olma şartını inceleyeceğiz. Son olarak bu koneksiyon ile verilen 3 boyutlu Quasi-Sasakian manifold hakkında bir örnek oluşturacağız.

Anahtar Kelimeler

Quarter-Simetrik Metrik Olmayan Koneksiyon , 3 boyutlu Quasi-Sasakian Manifold , $\eta $-paralel

Kaynakça

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