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A Schur Type Theorem for almost Alpha-Cosymplectic Manifolds with Kaehlerian Leaves.
(2014) Ayar, Gülhan
In this study, we give a shur type therom for almost alpha-cosymplectic manifolds with Kaelılerian leaves. We compute some curvature properties and we obtain plıi-holomorphic sectional curvature.
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.
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.
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.
Almost Cosymplectic (k,M)-Spaces Satisfying Some Curvature Conditions.
(2012) Aktan, N.; Bektas, I.; Ayar, Gülhan
In this stııdy, we concentratcon conformally flat, ^-conformally flat and C-Boclnıcr curvaturc tensors for almost cosymplectic (k, /ı)-spaces.
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.
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.
A Theorem of Schur Type for Almost Kenmotsu Manifolds with Kaehlerian Leaves.
(2013) Aktan, N.; Bektas, I.; Ayar, Gülhan
In 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.
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.
Some Structures on Nearly Cosymplectic Manifolds.
(2018) Yıldırım, M.; Ayar, Gülhan; Aktan, N.
The objective of the paper is to study on nearly cosymplectic manifolds admitting Ricci solitons. The study is organized as follows. After preliminaries we prove that if in a nearly cosymplectic manifold the metric g is a Ricci soliton and V is point-wise collinear with ?, then the manifold is an Einstein and Ricci soliton is shrinking. Also we show that an ?-Einstein nearly cosymplectic manifold admits a Ricci soliton (g,?,tr(h^2)) and Ricci soliton is shrinking.
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.
Some Soliton Conditions on Kenmotsu Manifolds.
(2018) Ayar, Gülhan; Karatas, S.; Aktan, N.
The geometry of Ricci solitons has been studied by many mathematicians. This paper deals with the study of Ricci solitons and gradient Ricci solitons in nearly Kenmotsu manifolds.
Nearly Cosymplectic Manifolds with Nullity Conditions
(2018) Yıldırım, M.; Ayar, Gülhan
We investigate nearly cosymplectic manifolds with k-nullity distribution. Also we consider pseudoprojectively flat N(k)-nearly cosymplectic manifolds.
On The Conharmonic Curvature Tensor of Nearly Cosymplectic Manifolds with Generalized Tanaka-Webster Connection Spaces.
(2021) Ayar, Gülhan; Çavusoglu, H. R.
Almost contact manifolds with Killing structures tensors were defined in [4] as nearly cosymplectic manifolds. Blair and Showers [4] studied nearly cosymplectic structure (o. & n. g) on a Riemannian manifold M with ? closed from the topological viewpoint. An almost contact metric structure (?. ? ?. g) satisfying (VxQ)X=0 is called a nearly cosymplectic structure[2]. In addition, a generalized Tanaka-Webster connection has been introduced by Tanno [5] as a generalization of Tabaka-Webster connection. Contact manifolds with generalized Tanaka-Webster connection were studied by many researchers In this study, based on previous works, we focus Tanaka-Webster connection on nearly cosymplectic manifolds and we obtain some results. Also we study conharmonic curvature tensor of nearly cosymplectic manifolds with generalized Tanaka-Webster connection and we give a conharmonically flat nearly cosymplectic manifold with respect to the connection V.
Etha-Ricci Soliton in Kenmotsu Manifold.
(2019) Yıldırım, M.; Ayar, Gülhan
In this paper we give a characterisation of ?-Ricci solitons in Ricci recurrent and recurrent Kenmotsu manifold based on the 1 form.
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.
Some Relations Between Curvature Tensors of a Riemannian Manifold.
(2017) Ayar, Gülhan; Tekin, P.; Aktan, N.
In this paper, properties alpha-cosymplectic manifolds equipped with M-procetive curvature tensor are studied. First, we gave the basic definitions and curvature properties of alpha-cosymplectic manifolds, then, we gave the definitions of Weyl projective curvature tensor , con-circular curvature tensor C and conformal curvature tensor V and we obtain some relations between these curvature tensors of a Riemannian manifold. Also we proved that an 2n+1-dimensional alpha-cosymplectic manifold is projectively flat if and only if it is either locally isometric to the hyperbolic space Hn(-1) . And finally, we proved that the M-projective curvature tensor in an alpha-cosymplectic manifold M is irrotational if and only if it is locally isometric to the hyperbolic space Hn(-a^2) .
On Some Curvature Conditions of Nearly Alpha-Cosymplectic Manifolds.
(2019) Ayar, Gülhan; Demirhan, D.
In the present study, we have focused on nearly alpha cosymplectic manifolds. After defining nearly ??cosymplectic manifolds, we have tried to show certain curvature conditions and basic properties of nearly ??cosymplectic manifolds.
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.
Primality Test with Singular Curves
(2019) Ayar, Gülhan; Özdemir, E.; Nari, K.
In this work, we develop a method to determine a given odd integer n = 3 mod 4 is prime or not. The method will be based on already presented an algorithm for he integers n = 1 mod 4. Prime integers are main ingredient of the most popular public key cryptosystems like RSA and Elliptic Curve Cryptosystem. For example, a secure design of an RSA cryptosystem requires prime integers with at least 300 digits. After being employed in cryptography, the prime integers and primality test has been rigorously studied by many researchers. Even though, there are 3 main algorithms being used in practice, finding a practical and deterministic primality test is still considered to be an important problem. In this work, we extend the primality test algorithm for n = 1 mod 4 to cover all integers i.e. for n = 3 mod 4. (Received September 22, 2018)

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