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Öğe A study on pseudoparallel submanifolds of generalized Lorentz-Sasakian forms(Univ Nis, Fac Sci Math, 2024) Pandey, Shashikant; Mert, Tugba; Atceken, Mehmet; Uygun, PakizeIn this article, pseudoparallel submanifolds for generalized Lorentz-Sasakian space forms are investigated. Submanifolds of these manifolds with properties such as pseudoparallel, 2-pseudoparallel, Ricci generalized pseudoparallel, and 2-Ricci generalized pseudoparallel have been investigated and the conditions under which these pseudoparallel submanifolds are totally geodesic are shown. In addition, necessary and sufficient conditions have been obtained for these submanifolds to be totally geodesic by means of the concircular, projective and quasi-conformally curvature tensors. At last, we provide an example for such manifold.Öğe Certain Curvature Conditions on $(k,\mu )$-Paracontact Metric Spaces(Emrah Evren KARA, 2022) Uygun, Pakize; Dirik, Süleyman; Atçeken, Mehmet; Mert, TuğbaThe aim of this paper is to classify $(k,\mu)$-paracontact metric spaces satisfying certain curvature conditions. We present the curvature tensors of (k,$\mu $)-Paracontact manifold satisfying the conditions $R\cdot W_{6}=0$, $ R\cdot W_{7}=0$, $R\cdot W_{8}=0$ and $R\cdot W_{9}=0$. According these cases, $(k,\mu)$-Paracontact manifolds have been characterized. Also, several results are obtained.Öğe Certain Results for Invariant Submanifolds of an Almost ?-Cosymplectic (k, µ, ?)-Space(Murat TOSUN, 2024) Uygun, Pakize; Atçeken, Mehmet; Mert, TuğbaIn this paper we present invariant submanifolds of an almost ?-cosymplectic (k, µ, ?)-space. Then, we gave some results for an invariant submanifold of an almost ?-cosymplectic (k, µ, ?)-space to be totally geodesic. As a result, we have discovered some interesting conclusions about invariant submanifolds of an almost cosymplectic (k, µ, ?)-space. © MSAEN.Öğe Invariant pseudoparallel submanifold of an SQ-Sasakian manifolds(Walter De Gruyter Gmbh, 2024) Atceken, Mehmet; Mert, Tugba; Uygun, PakizeThe aim of the present paper is to study invariant pseudoparallel submanifolds in an SQ-Sasakian manifold with respect to semisymmetric metric connection. We search the necessary and sufficient conditions for an invariant submanifold to be totally geodesic under the some hypotheses.Öğe Normal paracontact metric space form on $W_0$-curvature tensor(Amasya Üniversitesi, 2023) Mert, Tuğba; Atçeken, Mehmet; Uygun, PakizeIn this article, normal paracontact metric space forms are investigated on $W_0$-curvature tensor. Characterizations of normal paracontact space forms are obtained on $W_0$-curvature tensor. Special curvature conditions established with the help of Riemann, Ricci, and concircular curvature tensors are discussed on $W_0$-curvature tensor. Through these curvature conditions, some important characterizations of normal paracontact metric space forms are obtained. Finally, the need for further research is discussed.Öğe On Almost C(?)-Manifold Satisfying Certain Curvature Conditions(2024) Mert, Tuğba; Atçeken, Mehmet; Uygun, PakizeThis research article is about the geometry of the almost C(?)- manifold. Some important properties of the almost C(?)- manifold with respect to the W_3- curvature tensor, such as W_3-flat and W_3- semi-symmetry, are investigated. The relationship of W_3- curvature tensor with Riemann, Ricci, projective, concircular and quasi-conformal curvature tensor is discussed on the almost C(?)- manifold and many important results are obtained. In addition, W_3- pseudo symmetry and W_3- Ricci pseudo symmetry are investigated for the almost C(?)- manifold. The results obtained are interesting and give an idea about the geometry of the almost C(?)- manifold.Öğe On Invariant Submanifolds of Lorentz Sasakian Space Forms(Islamic Azad Univ, Shiraz Branch, 2023) Mert, Tugba; Atceken, Mehmet; Uygun, PakizeIn this article, invariant submanifolds of Lorentz-Sasakian space forms on the W-7- curvature tensor are investigated. For the W-7-curvature tensor, the pseudoparallel, 2-pseudoparallel, Ricci generalized pesudoparallel and 2-Ricci generalized pseudoparallel properties of the invariant submanifolds of the Lorentz-Sasakian space form are discussed.Öğe Pseudosymmetric Almost α-Cosymplectic (κ, μ, v)-Spaces Admitting Einstein Solitons(Rgn Publ, 2024) Atceken, Mehmet; Mert, Tugba; Uygun, PakizeThis paper attempts to characterize cases of an almost alpha alpha-cosymplectic (kappa, mu, nu)-space admitting Einstein sloitons to be concircular Ricci pseudosymmetry, projective Ricci pseudosymmetry, W-1-curvature and the W-2-curvature Ricci pseudo symmetric.Öğe Ricci Solitons on Pseudosymmetric $(\kappa,\mu)$-Paracontact Metric Manifolds(Salim YÜCE, 2024) Atçeken, Mehmet; Mert, Tuğba; Uygun, PakizeThe object of the present paper is to study some types of Ricci pseudosymmetric $(\kappa,\mu)$-paracontact metric manifolds whose metric admits Ricci soliton. We researched the conditions when Ricci soliton on Ricci pseudosymmetric, concircular Ricci pseudosymmetric, $W_3$-Ricci pseudosymmetric, Weyly projective Ricci pseudosymmetric and conharmonic Ricci pseudosmettric conditions on a $(\kappa,\mu)$-paracontact metric manifold. According to these conditions, we have evaluated the manifold to be shrinking, steady and expanding. Finally, we have also constructed a non-trivial example of $(\kappa,\mu)$-paracontact metric manifolds whose metric admits Ricci soliton and found the functions for the Ricci pseudosymmetric conditions.Öğe Semi-Symmetric Generalized Sasakian Space Forms On Some Special Curvature Tensors(Prof. Dr. Mehmet Zeki SARIKAYA, 2022) Mert, Tuğba; Atçeken, Mehmet; Uygun, PakizeIn this article, semi-symmetric generalized Sasakian space forms are investigated on some special curvature tensors. Characterizations of generalized Sasakian space forms are obtained on some specially selected ??curvature tensors. By examining the flatness of these ??curvature tensors, the properties of generalized sasakian space forms are given. More importantly, the cases of ??semi-symmetric generalized Sasakian space forms are discussed and the behavior of the manifold is examined for each case. Again, necessary and sufficient conditions have been obtained for ??symmetric generalized Sasakian space forms to be Einstein manifolds. © 2022, Prof. Dr. Mehmet Zeki SARIKAYA. All rights reserved.
