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Öğe ALMOST KENMOTSU f-MANIFOLDS(Vasyl Stefanyk Precarpathian Natl Univ, 2015) Balkan, Yavuz Selim; Aktan, NesipIn this paper we consider a generalization of almost Kenmotsu f-manifolds. We get basic Riemannian curvature, sectional curvatures and scalar curvature properties of such type manifolds. Finally, we give two examples.Öğe Chen's Type Inequality forWarped Product Pseudo-slant Submanifolds of Kenmotsu f-manifolds(Univ Nis, Fac Sci Math, 2019) Balkan, Yavuz Selim; Alkhaldi, Ali H.In the present paper, we consider non-trivial warped product pseudo slant submanifolds of type M-perpendicular to X-f M-theta and M-theta X-f M-perpendicular to of Kenmotsu f-manifold (M) over bar. Firstly, we get some basic properties of these type warped product submanifolds. Then, we prove the general sharp inequalities for mixed totally geodesic warped product pseudo slant submanifolds and also we consider equality cases. Also generalizes some previous inequalities as well.Öğe A CLASS OF phi-RECURRENT ALMOST COSYMPLECTIC SPACE(Honam Mathematical Soc, 2018) Balkan, Yavuz Selim; Uddin, Siraj; Alkhaldi, Ali H.In this paper, we study phi-recurrent almost cosymplectic (k, mu)-space and prove that it is an eta-Einstein manifold with constant coefficients. Next, we show that a three-dimensional locally phi-recurrent almost cosymplectic (k, mu)-space is the space of constant curvature.Öğe Generalized Inequalities of Warped Product Submanifolds of Nearly Kenmotsu f-Manifolds(Univ Nis, Fac Sci Math, 2019) Balkan, Yavuz Selim; Alkhaldi, Ali H.; Siddiqui, Aliya Naaz; Ali, AkramIn the present paper, we establish two general sharp inequalities for the squared norm of second fundamental form for mixed totally geodesic warped product pseudo-slant submanifolds of the form M-perpendicular to x(f) M-theta and M-theta x(f) M-perpendicular to, in a nearly Kenmotsu f-manifold (M) over bar, which include the squared norm of the warping function and slant angle. Also, equality cases are verified. We proved that some previous results are trivial from our results. Moreover, we generalized the inequality theorems [3] and [26] from our derived results.Öğe Geometry of Warped Product Pointwise Submanifolds of Sasakian Manifolds(Univ Nis, Fac Sci Math, 2020) Alqahtani, Lamia Saeed; Balkan, Yavuz SelimRecently, Chen and Uddin introduced and studied warped product pointwise bi-slant subman-ifolds of Kahler manifolds in [13]. They have obtained many interesting results. In the present paper, we investigate warped product pointwise bi-slant submanifolds in Sasakian manifolds and we derive contact version of results obtain in [13]. We give a non-trivial example to prove the existence of these submanifolds.Öğe Hemen hemen kenmotsu f-manifoldların bir genelleştirilmesi(Düzce Üniversitesi, 2013) Balkan, Yavuz Selim; Aktan, NesipBu tez çalışması dört bölümden oluşmaktadır. Birinci bölüm, giriş kısmına ayrılarak genel bir literatür bilgisi verilmiştir. İkinci bölümde, gerekli temel kavramlardan söz edilmiştir. Üçüncü bölümde, hemen hemen Kenmotsu f-manifoldlar için eğrilik özellikleri verilerek hemen hemen Kenmotsu f-manifoldların bir genelleştirilmesi yapılmıştır. Son bölüm olan dördüncü bölüm ise sonuç ve önerilere ayrılarak, konu ile ilgili açık problemlere yer verilmiştir.Öğe A New Class of f-Structures Satisfying f(3) - f=0(Univ Nis, Fac Sci Math, 2018) Balkan, Yavuz Selim; Uddin, Siraj; Stankovic, Mica S.; Alkhaldi, Ali H.In this study, we introduce a new class of pseudo f-structure, called hyperbolic f-structure. We give some classifications of this new structure. Further, we extend the notion of (kappa, mu, nu)-nullity distribution to hyperbolic almost Kenmotsu f-manifolds. Finally, we construct some non-trivial examples of such manifolds.Öğe On A New Type of (k, mu)-Contact Metric Manifolds(Amer Inst Physics, 2017) Balkan, Yavuz Selim; Ayar, Gülhan; Aktan, Nesipn the present paper we introduce cyclic-parallel t-curvature tensor on (k, mu)-contact metric manifolds. We investigate some curvature properties of these type manifolds and we obtain that these type of manifolds have cyclic-parallel Ricci tensor under some conditions. Furthermore, we get these type of manifolds are K-contact under some special cases and we obtain that M is locally isometric to the product En+1 x S-n (4) under some algebraic conditions.Öğe Some Symmetry Properties of Almost S-Manifolds(2017) Balkan, Yavuz Selim; Sarıkaya, Mehmet ZekiManifold theory is an important topic in differential geometry. Riemannian manifolds are a wide class of differentiable manifolds. Riemannian manifolds consist of two fundamental class, as contact manifolds and complex manifolds. The notion of globally framed metric f -manifold is a generalization of these fundamental classes. Almost S -manifolds which are globally framed metric f -manifold generalize some contact manifolds carrying their dimension to (2n s). On the other hand, classification is important for Riemannian manifolds with respect to some intrinsic and extrinsic tools as well as all sciences. Moreover, symmetric manifolds play an important role in differential geometry. There are a lot of symmetry type for Riemannian manifolds with respect to different arguments. Under these considerations, in the present paper we study some symmetry conditions on almost S -manifolds. We investigate weak symmetries and ? - symmetries of these type manifolds. We obtain some necessary and sufficient conditions to characterize of their structures. Firstly, we prove that the existence of weakly symmetric and weakly Ricci symmetric almost S -manifolds under some special conditions. Then, we show that every ? -symmetric almost S -manifold verifying the (?,µ)-nullity distribution is an ? -Einstein manifold of globally framed type. Finally, we get some necessary and sufficient condition for a ? -Ricci symmetric almost S -manifold verifying the (?,µ) -nullity distribution to be an ? -Einstein manifold of globally framed type.Öğe Yaklaşık C-manifoldların geometrisi(Düzce Üniversitesi, 2016) Balkan, Yavuz Selim; Aktan, NesipBu tez çalışmasında, yaklaşık manifoldların yeni bir sınıfı olan yaklaşık C-manifoldların tanımı verilmiş ve bazı eğrilik özellikleri elde edilmiştir. Elde edilen bazı özellikler, verilen örnekler üzerinde hesaplanmıştır. Ayrıca bu yeni sınıfın bazı alt manifoldları çalışılmıştır. Öte yandan yaklaşık C-manifoldların sağladığı özelliklerin, bazı D-konformal dönüşümler altında değişmez kalıp kalmadığı incelenmiştir. Bu yeni manifold sınıfı üzerinde Ricci solitonlar göz önüne alınarak bazı sınıflandırılmaları yapılmıştır. Yaklaşık C-manifoldlar genelleştirilmiş S-uzay formların alt manifoldları olarak ele alınmıştır. Son olarak bu yaklaşık C-alt manifoldların bazı sınıflandırmalarına yer verilmiştir.
