@article{article_1699264, title={The Application of A New Type of Connection on $3$-dimensional Quasi-Sasakian Manifolds}, journal={Journal of Engineering Technology and Applied Sciences}, volume={10}, pages={71–96}, year={2025}, DOI={10.30931/jetas.1699264}, author={Çetinkaya, Azime}, keywords={Quarter-Simetrik Metrik Olmayan Koneksiyon, 3 boyutlu Quasi-Sasakian Manifold, $\eta $-paralel}, 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.}, number={2}, publisher={Muhammet KURULAY}