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Öğe A New Class of Nearly Kenmotsu Manifolds(2018) Tekin, P.; Ayar, Gülhan; Aktan, N.The aim of this work is to show that, in ? Einstein nearly Kenmotsu manifolds with projective curvature tensor , and conharmonic curvature tensor , satisfy the conditions R(X ,Y ).P = 0 and R(X ,Y ).N = 0 respectively. And so, to obtain a new class of ? Einstein nearly Kenmotsu manifolds.Öğe A New Type of Almost Contact Manifolds.(2016) Ayar, Gülhan; Carriazo, A.; Aktan, N.The purpose of this paper is to study the Singuler Semi-Riemannian Almost Contact manifolds, The geometry of manifolds with degenerate indefnite metrics has becn studied by Demir Küpeli [I]. In that book it is shown that a manifold M with a degenerate indefinit metric g admits a geometric structure if and only if g is Lie parallel along the vector fields on M. In this case we call (M, g) a Singular Semi-Riemannian manifold. Then it is possible to attach a nondegenerate tangent bundle to (M, g) which admits a connection whose curvature tensor satisfies the usual identities of the curvature tensor of Levi Civita connection. We cald this connection the Kozsul Connection of (M, g). In this talk we will present Singuler Semi-Riemannian manifolds (introduced by Demir Küpeli in [1] ) with an adapted almost contact strueture. We will study the main facts about such a structure, with some examples.Öğe A Schur Type Theorem For Almost Cosymplectic Manifolds With Kaehlerian Leaves.(2013) Aktan, N.; Ayar, Gülhan; Bektas, I.In this study, we give a Schur type theorem for almost cosymplectic manifolds with Keahlerian leaves.Öğe A Theorem of Schur Type for Almost Kenmotsu Manifolds with Kaehlerian Leaves.(2013) Aktan, N.; Bektas, I.; Ayar, GülhanIn this study, we concentrate on almost Kenmotsu manifolds with Kaehlerian leaves and considering Schur’s lemma on spaces of constant curvature, we get a new version for almost Kenmotsu manifolds with Kaehlerian leaves.Öğe Almost Cosymplectic (k,M)-Spaces Satisfying Some Curvature Conditions.(2012) Aktan, N.; Bektas, I.; Ayar, GülhanIn this stııdy, we concentratcon conformally flat, ^-conformally flat and C-Boclnıcr curvaturc tensors for almost cosymplectic (k, /ı)-spaces.Öğe Almost Cosymplectic Manifolds of Constant Phi-Sectional Curvature.(2012) Aktan, N.; Ayar, Gülhan; Bektas, I.The object of the paper is to give a new version of Schur’s lemma on spaces of constant curvature for almost cosymplectic manifolds with Kaehlerian leaves.Öğe Concircular Curvature Tensor of Nearly Cosymplectic Manifolds in Terms of The Generalized Tanaka-Webster Connection(2024) Ayar, Gülhan; Aktan, N.; Madan, Ç.In this paper, we study concircular curvature tensor of nearly cosymplectic manifolds in terms of the generalized Tanaka-Webster connection and then, we emphasized the properties that concircular curvature tensor of nearly cosymplectic manifolds in terms of the generalized Tanaka-Webster connection provides in case of flatness, ?-concircularly flatness, ?-concircularly semisymmetric.Öğe Concircular Curvature Tensor of Nearly Cosymplectic Manifolds with Generalized Tanaka-Webster Connection.(2021) Madan, Ç.; Ayar, Gülhan; Aktan, N.The aim of this study is to research concircular curvature tensor of nearly cosymplectic manifolds with generalized Tanaka-Webster connection. With this study, we have focused on the important curvature properties of nearly cosymplectic manifolds equipped with Tanaka-Webster connection. Also, based on these curvature properties, we have defined the concircular curvature tensor with respect to the generalized Tanaka-Webster connection. Then, we emphasized the properties that concircular curvature tensor of nearly cosymplectic manifolds with Tanaka-Webster connection provides in case of flatness, ?-concircularly flatness, ?-concircularly semisymmetric.Öğe Eta-Ricci Solitons and Gradient Ricci Solitons On Nearly Kenmotsu Manifolds.(2018) Ayar, Gülhan; Yıldırım, M.; Aktan, N.In this paper, we study Ricci solitons and gradient Ricci solitons on nearly Kenmotsu manifolds. After giving some basic definitions, we prove that in a nearly Kenmotsu manifold, if the metric g admits a Ricci soliton (g,v, ?) and V is pointwise collinear with ? , then the manifold is an ?-Einstein manifold and, in particular, an Einstein manifold. Moreover, we show that if a nearly Kenmotsu manifold admits a compact Ricci soliton, then the manifold is Einstein. Finally, we prove that if an ?-Einstein nearly Kenmotsu manifold admits a gradient Ricci soliton, then the manifold reduces to an Einstein manifold under certain conditions.Öğe Eta-Ricci Solitons on Nearly Cosymplectic Manifolds.(2018) Yıldırım, M.; Ayar, Gülhan; Aktan, N.The present paper deals with the study of ? -Ricci solitons on nearly cosymplectic manifolds admitting some geometric conditionsÖğe Geometry of Kenmotsu Manifolds via Q-Curvature Tensor and Schouten–Van Kampen Connection.(2025) Yıldırım, M.; Beyendi, S.; Ayar, Gülhan; Aktan, N.This research paper aims to study the Q-curvature tensor on Kenmotsu manifolds endowed with the Schouten–van Kampen connection. Using the Q-curvature tensor, whose trace is the well-known Z-tensor, we characterized Kenmotsu manifolds by introducing the notion of ?-Q flat and ?-Q flat manifolds and novel tensor conditions, such as Q(?,X)Q=0, Q(?X)R=0, Q(?,X)S=0, Q(?,X)C=0 ,Q(?,X)H=0, and Q(?,X)P=0, with the Schouten–van Kampen connection. To validate some of our results, we constructed a non-trivial example of Kenmotsu manifolds endowed with the Schouten–van Kampen connection.Öğe Nearly Cosymplectic Manifolds with Tanaka-Webster Connection.(2021) Madan, Ç.; Ayar, Gülhan; Aktan, N.The aim of this study is to research concircular curvature tensor of Nearly cosymplectic manifolds with Tanaka-Webster Connection. We defined The concir-cular curvature tensor with respect to the generalized Tanaka-Webster connection. Also in this work, we studied concircularly flat, ?-concircularly flat, ?-concircularly flat, pseudo-concircularly flat and we have shown some equations.Öğe On a Type of ?-Cosymplectic Manifolds.(2019) Beyendi, S. ,; Ayar, Gülhan; Aktan, N.The ob ject of this paper is to study alpha-cosymplectic manifolds admitting a W2-curvature tensor.Öğe On Almost Alpha-Cosymplectic Manifolds With M-Projective Curvature Tensor.(2017) Ayar, Gülhan; Aktan, N.In this paper, we study almost alpha-cosymplectic manifolds with M projective curvature tensor and we obtain the relation between different curvature tensors.Öğe On Einstein Nearly Cosymplectic Manifolds(2018) Tekin, P.; Ayar, Gülhan; Aktan, N.This paper deals with the study of Einstein nearly cosymplectic manifold which has projective curvature tensor P and conharmonic curvature tensor N, satisfying R(X,Y)P=0 and R(X,Y)N=0 respectively. Moreover we have shown that Einstein nearly cosymplectic manifold has 5 dimension.Öğe On Nearly Kenmotsu Manifolds Admitting Some Geometric Conditions.(2018) Ayar, Gülhan; Yıldırım, M.; Aktan, N.In this paper we study ?–Ricci solitons on nearly Kenmotsu manifolds admitting some geometric conditions. After we review some preliminary results, we give the existence of ?–Ricci solitons on nearly Kenmotsu manifolds. We study existence of ?–Ricci solitons on nearly Kenmotsu manifold satisfying Ricci-semisymmetry condition. Then we consider ?–Ricci solitons on nearly Kenmotsu manifold satisfying S.R=0, Einstein semisymmetry and partially Ricci-pseudosymmetry conditions respectively.Öğe On Singular semi-Riemannian Almost Contact Manifolds.(2017) Ayar, Gülhan; Carriazo, A.; Aktan, N.In this contribution we introduce and study singular semi-Riemannian aimost contact manifolds, by considcring Demir Kupeli’s book on singular semi-Riemannian geometry [5]. We also provide somc examples.Öğe Ricci Solitons on Nearly Kenmotsu Manifolds(2018) Ayar, Gülhan; Yıldırım, M.; Aktan, N.In this study Ricci solitons and gradient Ricci solitons in a nearly Kenmotsu manifold are investigated. After giving preliminaries and some definitions we have proved that in a nearly Kenmotsu manifold if the metric admits a Ricci soliton then the manifold is an n-Einstein manifold. In addition to these, we have showed that if a nearly Kenmotsu manifold admits a compact Ricci soliton, then the manifold is Einstein. Finally we have proved that if an n-Einstein nearly Kenmotsu manifold admits a gradient Ricci soliton, then the manifold reduces to an Einstein manifold under certain conditionÖğe Singular Semi-Riemannian Almost Contact Manifolds.(2015) Ayar, Gülhan; Carriazo, A.; Aktan, N.İn this talk we will present singular semi-Riemannian manifolds (introduced by D. N. Kııpeli in [1]) with an adapted almost contact structure. We will study the main facts about such a structure, with some examples. Finally, we will focus on some curvature properties.Öğe Some Curvature Condition On Nearly Cosymplectic Manifolds.(2017) Ayar, Gülhan; Yıldırım, M.; Aktan, N.In this study, we investigated the properties of nearly cosymplectic manifolds equipped with M-projective curvature tensor.
