Barman, Ajit; Ünal, Inan

In this paper, we study Riemannian manifolds admitting a type of semi-symmetric nonmetric connection. By taking the characteristic vector field of this connection as a parallel vector field via the Levi-Civita connection, we examine some curvature properties of Riemannian manifolds. We discuss Ricci-semi symmetry and we consider the conformal curvature tensor. Finally, we study hypersurfaces of Riemanninan manifolds admitting a type of semi-symmetric non-metric connection with a parallel characteristic vector field. We take an example of a Riemannian manifold and we apply our results.

İncele

Altin, Mustafa; Yoldas, Halil Ibrahim; Ünal, Inan

In this study, some geometric properties of N(k)-contact metric manifolds, which are important class of contact manifolds, have been investigated by using a special connection (CY-connection). First, we give some fundamental results on N(k)-contact metric manifolds admitting CY-connection. Then, we obtain curvature properties of such manifolds. We prove that an N(k)-contact metric manifold admitting R* (xi, X).R* = 0 condition is an N (-1/4) metric manifold, where R* is the Riemannian curvature tensor of CY-connection. Also, we examine an N(k)-contact metric manifold admitting CY-connection under W* (xi, X).S* = 0 condition for generalized quasi-conformal curvature tensor W* of CY-connection. Finally, we consider a 3-dimensional N(k)-contact metric manifold admitting CY-connection.

İncele

Vanli, Aysel Turgut; Ünal, Inan

In this paper, we study on semi-invariant submanifolds of normal complex contact metric manifolds. We give the definition of such submanifolds and we obtain useful relations. Moreover, we give the integrability conditions of distributions.

İncele

Ünal, Inan

Blair et al. [7] introduced the notion of bicontact manifold in the context of Hermitian geometry. Bande and Hadjar [1] studied on this notion under the name of contact pairs. These type of structures have important properties and their geometry is some different from classical contact structures. In this paper, we study on some semi-symmetry properties of the normal contact pair manifolds. We prove that a Ricci semi-symmetric (or concircularly Ricci semi-symmetric) normal metric contact pair manifold is a generalized quasi-Einstein manifold. Also, we classify normal metric contact pair manifolds as a generalized quasi-Einstein manifold with certain semi-symmetry conditions L (X, Z).R = 0, R(X, Z).L = 0 and L (X, Z).L = 0 for the concircular curvature tensor L, the Riemannian curvature tensor R, and an arbitrary vector field X.

İncele

Ünal, Inan

In this paper, the geometry of normal metric contact pair manifolds is studied under the circle divide atness of conformal, concircular and quasi-conformal curvature tensors. It is proved that a conformal flat normal metric contact pair manifold is an Einstein manifold with a positive scalar curvature and has positive sectional curvature. It is also shown that a concircular flat normal metric contact pair manifold is an Einstein manifold. Finally, it is obtained that a quasi-conformally flat normal metric contact pair manifold is an Einstein manifold with a positive scalar curvature and, is a space of constant curvature.

AtıfOpenAlex4·TR Dizin3

İncele

Altin, Mustafa; Ünal, Inan

In this paper we tried to find parametric presentation of a surface family with common line of curvature in 3-dimensional Galilean space. We have obtained necessary and sufficient conditions for the curve to be a common line of curvature on this surface. We have stated examples to visualize our results and also, we have examined a torsion free curve.

AtıfWoS1·OpenAlex2

İncele

Ünal, Inan

In this study, we investigate generalized quasi-Einstein normal metric contact pair manifolds. Initially, we deal with the elementary properties and existence of generalized quasi-Einstein normal metric contact pair manifolds. Later, we explore the generalized quasi-constant curvature of normal metric contact pair manifolds. It is proved that a normal metric contact pair manifold with generalized quasi-constant curvature is a generalized quasi-Einstein manifold. Normal metric contact pair manifolds satisfying cyclic parallel Ricci tensor and the Codazzi type of Ricci tensor are considered, and further prove that a generalized quasi-Einstein normal metric contact pair manifold does not satisfy Codazzi type of Ricci tensor. Finally, we characterize normal metric contact pair manifolds satisfying certain curvature conditions related toM-projective, conformal, and concircular curvature tensors. We show that a normal metric contact pair manifold with generalized quasi-constant curvature is locally isometric to the Hopf manifold S2n+1(1) x S1.

AtıfScopus5·WoS3·OpenAlex4

İncele

Vanli, Aysel Turgut; Ünal, Inan; Özdemir, Dilek

In this paper, we study on normal complex contact metric manifold admitting a semi symmetric metric connection. We obtain curvature properties of a normal complex contact metric manifold admitting a semi symmetric metric connection. We also prove that this type of manifold is not conformal flat, concircular flat, and conharmonic flat. Finally, we examine complex Heisenberg group with the semi symmetric metric connection.

AtıfScopus24·WoS25·OpenAlex26

İncele

Ünal, Inan; Yildirim, Ozal; Ozyildirim, BM; Yildirim, T

Deep learning algorithms have recently become the most widely used machine learning approaches. Remarkable approaches have emerged in the field of machine learning studies with the use of geometric methods for deep learning. The manifold theory, which is simply regarded as the general state of an Euclidean space, has become applicable in the field of deep learning and this field has been named Geometric Deep Learning. In this study, applications of manifold theory and differential geometry to deep learning is presented.

İncele