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    A note on P-Sasakian manifolds satisfying certain conditions
    (Universidad Catolica del Norte, 2024) Uygun, Pakize; Atçeken, Mehmet
    In the present paper, we have studied the curvature tensors of P-Sasakian manifold. For a P-Sasakian manifold, (Formula presented) and W9 · W1 = 0 cases are considered. According these cases, P-Sasakian manifolds have been characterized such as ?-Einstein and Einstein. In addition, we research W1-flat and W9-flat for a P-Sasakian manifold. The results are interesting and give an idea about the geometry of P-Sasakian manifold.
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    A study on pseudoparallel submanifolds of generalized Lorentz-Sasakian space forms
    (University of Nis, 2024) Pandey, Shashikant; Mert, Tuğba; Atçeken, Mehmet; Uygun, Pakize
    In 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.
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    Certain Results for Invariant Submanifolds of an Almost ?-Cosymplectic (k, µ, ?)-Space
    (Murat TOSUN, 2024) Uygun, Pakize; Atçeken, Mehmet; Mert, Tuğba
    In this paper we present invariant submanifolds of an almost alpha-cosymplectic (k,mu,nu)-space. Then, we gave some results for an invariant submanifold of an almost alpha-cosymplectic (k,mu,nu)-space to be totally geodesic. As a result, we have discovered some interesting conclusions about invariant submanifolds of an almost cosymplectic (k,mu,nu)-space.
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    Invariant pseudoparallel submanifold of an SQ-Sasakian manifolds
    (Walter de Gruyter GmbH, 2025) Atçeken, Mehmet; Mert, Tuğba; Uygun, Pakize
    The 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.
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    New insights on pseudoparallel submanifold in trans Sasakian manifolds
    (University of Nis, 2025) Atçeken, Mehmet; Mert, Tuğba; Uygun, Pakize; Stanković, Mića S.
    The aim of the present paper is to study invariant pseudo-parallel submanifolds of a trans Sasakian manifold. We have searched the necessary and sufficient conditions for an invariant pesudo-parallel submanifold to be totally geodesic under the some conditions.
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    On (k,mu)-Paracontact Manifold Satisfying Some Curvature Conditions
    (Matematikçiler Derneği, 2023) Uygun, Pakize; Atçeken, Mehmet
    In this work, we studied the curvature tensors of (k,mu) satisfying the conditions widetildeZ(xi,alpha3)cdotP=0, widetildeZ(xi,alpha3)cdotS=0, R(xi,alpha3)cdotP=0, R(xi,alpha3)cdotS=0 and PcdotC=0. Besides this, we classify (k,mu)-paracontact manifolds. Also we researched conformally flat and phi-conformally flat a (k,mu)?paracontact metric manifolds.
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    On Invariant Submanifolds of Lorentz Sasakian Space Forms
    (Islamic Azad University Shiraz Branch, 2023) Mert, Tuğba; Atçeken, Mehmet; Uygun, Pakize
    n 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.
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    On kenmotsu metric spaces satisfying some conditions on the W1-Curvature tensor
    (University of Nis, 2022) Uygun, Pakize; Atçeken, Mehmet; Dirik, Süleyman
    In this paper we present the curvature tensors of Kenmotsu manifold satisfying the conditions W1 (X, Y) · W0 = 0, W1 (X, Y) · W1 = 0, W1 (X, Y) · W2 = 0, W1 (X, Y) · W3 = 0, W1 (X, Y) · W4 = 0 and W1 (X, Y) · W? = 0. According to these cases, Kenmotsu manifolds have been characterized. We consider 1 that some interesting results on a Kenmotsu metric manifold are obtained.
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    Pseudosymmetric Almost α-Cosymplectic (κ, μ, v)-Spaces Admitting Einstein Solitons
    (RGN Publications, 2024) Atçeken, Mehmet; Mert, Tuğba; Uygun, Pakize
    This 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.
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    Rigidity results for submanifolds in generalized Sasakian space forms
    (Universidad Catolica del Norte, 2023) Mert, Tuğba; Atçeken, Mehmet; Uygun, Pakize
    In this article, generalized Saasakian space forms are discussed and invariant submanifolds of these space forms are examined. The curvature tensor chosen is of great importance when examining the characterization of a manifold. In this article, invariant submanifolds of generalized Sasakian space forms are characterized according to the W*0?curvature tensor and pseudoparallel submanifolds are investigated for these space forms.
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    Semi-symmetric almost c(?)-manifold on some curvature tensors
    (Canadian University of Dubai, 2023) Mert, Tuğba; Atçeken, Mehmet; Uygun, Pakize
    In this article, semi-symmetry of almost C (?)-manifold is investigated on some special curvature tensors. First, the behavior of the almost C (?)-manifold is investigated when the special curvature tensors discussed are flat. Then, for these special curvature tensors, the behavior of the manifold in the semi-symmetric condition is observed and for some special curvature ten-sors, important properties such as the semi-symmetric almost C (?)-manifold being Einstein and ??Einstein manifold are obtained.
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    Semi-Symmetric Lorentz-Sasakian Space Forms and Some Special Curvature Tensors
    (Southeast Asian Mathematical Society, 2025) Mert, Tuğba; Atçeken, Mehmet; Uygun, Pakize
    In this article, the concept of semi-symmetry for Lorentz-Sasakian space forms on some W-curvature tensors is investigated. Firstly, flatness and xi-flatness states of some W-curvature tensors are investigated. Then, characterization of Lorentz-Sasakian space forms in case of semi-symmetry is obtained for the W-curvature tensors considered.
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    Some characterizations for a (k, µ)-paracontact metric manifold to be an η-Einstein manifold
    (Palestine Polytechnic University, 2024) Uygun, Pakize; Atçeken, M.
    In this paper we introduce the curvature tensors of (k,µ)-paracontact manifold satisfying the conditions (formula presented) According these cases, (k, µ)-paracontact manifolds have been characterized such as η-Einstein.
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    Some results on invariant submanifolds of a paracontact (?, µ, ?)-space
    (University of Nis, 2023) Uygun, Pakize
    In this paper, we have characterized an invariant submanifold of a paracontact (?, µ, ?)-space. Besides this, we have researched some geometric conditions for an invariant submanifold of a paracontact (?, µ, ?)-space to be totally geodesic.