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

Abstract

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.

Keywords

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

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

Abstract

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.

Keywords

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

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