Ünal, İnan

Complex manifolds include different subclasses, and one of the most significant ones is the class of Kähler manifolds. These types of manifolds have valuable curvature properties that are related to almost complex structures. For this study, we focused on Kähler manifolds having semi-symmetry conditions associated with H-curvature tensors. Another important subclass is of IK-normal complex contact metric man-ifolds, which are complex manifolds with a contact structure. Since the complex structure of this type of manifold is Kähler, it has important ap-plications. In the last section, we used the results obtained for a Kähler manifold to an IK-normal complex contact metric manifold.

İncele

Ünal, İnan; Barman, Ajit; Prakasha, D.G.

This chapter explores Chen-Ricci inequalities for submanifolds of Kenmotsu space forms endowed with a ϕ−η-connection, a special type of quarter-symmetric metric connection. The geometric background of Kenmotsu space forms and the properties of the ϕ−η-connection are briefly introduced, followed by the derivation of relevant curvature relations. The study proceeds by examining submanifolds within this framework, focusing on the behavior of curvature tensors and associated Riemannian invariants. Using the properties of the ambient space and the chosen connection, several inequalities involving Chen invariants and Ricci curvatures are obtained.

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Ünal, İnan; Altın, Mustafa; Pandey, Shashikant

In this study, we consider various geometric conditions associated with the vanishing of a generalized curvature tensor, namely the T-tensor, on N(κ)-contact metric manifolds. We define and analyze several types of T-flatness conditions, including T-flat, ξ-T-flat, quasi-T-flat, and φ-T-flat structures. By applying these flatness conditions, we obtain algebraic constraints on the curvature parameters, particularly involving the Ricci tensor. The resulting characterizations allow for the classification of N(κ)-contact metric manifolds as either Einstein or η-Einstein, depending on the specific values of the structure constants. These investigations also lead to deeper insights into the geometric structure and local isometry types of the manifolds under study.

AtıfScopus1·OpenAlex1

İncele

Prakasha, D.G.; Deepika, M.V.; Ünal, İnan

In this study, we investigate Lorentzian para-Kenmotsu (LP-Kenmotsu (LPK)) manifolds in the context of the generalized Tanaka-Webster connection, denoted as D*. Initially, we derive the formulas for the curvature tensor, Ricci tensor, and scalar curvature of an LPK manifold with respect to the connection D*. We analyze the geometric properties of these manifolds, including their local symmetry, Ricci semi-symmetry, and local ψ-symmetry. Furthermore, utilizing the Q-curvature tensor, we analyze conditions under which LPK manifolds exhibit Q*-flatness, Q*-Ricci semi-symmetry, and ψ-Q*-flatness concerning the connection D*.

İncele

Prakasha, Doddabhadrappla Gowda; Bin Turki, Nasser; Veerabhadraswamy Deepika, Mathad; Ünal, İnan

In the current article, we examine Lorentzian para-Kenmotsu (shortly, LP-Kenmotsu) manifolds with regard to the generalized symmetric metric connection (Formula presented.) of type (Formula presented.). First, we obtain the expressions for curvature tensor, Ricci tensor and scalar curvature of an LP-Kenmotsu manifold with regard to the connection (Formula presented.). Next, we analyze LP-Kenmotsu manifolds equipped with the connection (Formula presented.) that are locally symmetric, Ricci semi-symmetric, and (Formula presented.) -Ricci symmetric and also demonstrated that in all these situations the manifold is an Einstein one with regard to the connection (Formula presented.). Moreover, we obtain some conclusions about projectively flat, projectively semi-symmetric and (Formula presented.) -projectively flat LP-Kenmotsu manifolds concerning the connection (Formula presented.) along with several consequences through corollaries. Ultimately, we provide a 5-dimensional LP-Kenmotsu manifold example to validate the derived expressions.

AtıfScopus3·OpenAlex1

İncele

Vasiulla, Mohd; Ali, Mohabbat; Ünal, İnan

In this paper, we explore a set of geometric properties of Mixed Super Quasi-Einstein (MSQE) manifolds and provide examples of both Riemannian and Lorentzian MSQE manifolds to demonstrate their existence. Furthermore, we examine MSQE spacetimes in the context of the space-matter tensor, discussing several related properties. Finally, we establish the existence of an MSQE spacetime through a nontrivial example.

AtıfScopus3·WoS4·OpenAlex2

İncele

Sari, Ramazan; Ünal, İnan

A Lorentzian para-Sasakian (LP-Sasakian) space form is a kind of para-Sasakian manifold with constant φ− holomorphic sectional curvature. The presented paper is on the curvatures of semi-invariant submanifolds of an LP-Sasakian space form. Firstly, the definition of a semi-invariant submanifold of LP-Sasakian space form is given and an example is presented. Then, some important results on Ricci and scalar curvatures have been obtained by using the Gauss equation related to curvatures. Furthermore, by suffering from these results, the conditions of a distribution is being Einstein have been examined. Finally, semi-invariant products of Lorentzian para-Sasakian manifolds have been considered and an important inequality for the second fundamental form is proved.

AtıfOpenAlex1·TR Dizin1

İncele

Barman, Ajit; Ünal, İnan

The object of this paper is to study Kenmotsu manifolds admitting Z−tensor, which is a generalization of Einstein tensor that comes from general rel-ativity. We define a special type of quarter-symmetric non-metric ϕ and η-connection on a Kenmotsu manifold and we examine some geometric properties of such manifolds with Z−tensor. Some semi-symmetry conditions related to Z−tensor are studied on Kenmotsu manifolds and finally, we ob-serve our results on a 5-dimensional Kenmotsu manifold.

AtıfScopus6

İncele

Sari, Ramazan; Ünal, İnan

In this study, we work on normal-metric contact pair manifolds under certain conditions related to the Ricci curvature. We obtain some results for generalized quasi-Einstein normal-metric contact pair manifolds. We prove that such manifolds are not pseudo-Ricci symmetric. Finally, we investigate Ricci solitons on normal-metric contact pair manifolds.

İncele

Turgut Vanlı, Aysel; Ünal, İnan; Avcu, Keziban

In this article, we study a class of normal complex contact metric manifold called a complex Sasakian manifolds. This kind of manifolds have a globally defined complex contact form and normal complex contact structure. We define a complex Sasakian manifold by considering the real case and we present general properties. Also, we obtain some useful curvature relations. Finally, we examine flatness conditions for general curvature tensor B.

AtıfScopus3·OpenAlex2

İncele

Ünal, İnan; Altın, Mustafa

In this paper, we characterize N(κ)-contact metric manifolds with generalized Tanaka-Webster connection.We obtain some curvature properties. It is proven that if an N(κ)-contact metric manifold with generalized Tanaka-Webster connection is K-contact then it is an example of generalized Sasakian space form. Also, we examine some flatness and symmetric conditions of concircular curvature tensor on an N(κ)-contact metric manifolds with generalized Tanaka-Webster connection.

AtıfScopus5·WoS1·OpenAlex2

İncele

Ünal, İnan; Sari, Ramazan

A para-Kenmotsu space form is a para-Kenmotsu manifold with constant φ− sectional curvature. In this study, we work on para-Kenmotsu space forms under some flatness conditions of generalized quasi-conformal curvature tensor which is a generalization of conformal, concircular, conharmonic, projective, M-projective and pseudo-projective curvature tensors. We examine GQC-flat and ξ−GQC flat p-Kenmotsu space forms.

AtıfScopus1

İncele

Ünal, İnan

Bu çalışmanın amacı, normal metrik kontakt çift (NMCP) manifoldlarını genelleştirilmiş quasi-conformal eğrilik(GQC) tensörünün sıfırlık koşulları altında incelemektir. Bu kapsamda GQC-düz ve GQC-Z-düz NMCP manifoldları ileilgilenilmiştir. Bir GQC-düz manifoldun genelleştirilmiş yarı-Einstein (GQE) manifold olduğu ve bu çeşit manifoldlarıngenelleştirilmiş yarı-sabit eğriliğe sahip olduğu ispatlanmıştır. Son olarak, GQC eğrilik tensörünün düzlük şartları altında,NMCP manifoldlarının kesitsel eğrilikleri ele alınmıştır.

AtıfTR Dizin1

İncele

Ünal, İnan; Sarı, Ramazan

In this paper, we present some new results on invariant submanifolds of a para-Sasakian manifold under the quasi-conformally flatness condition. Firstly, we examine flatness of quasi-conformal curvature tensor on para-Sasakian manifolds. We prove that a quasi-conformally flat para-Sasakian manifold is an η-Einstein manifold. Also, we give some results on the sectional curvature of such manifolds. Secondly, we consider the invariant submanifolds of a quasi-conformally flat para-Sasakian manifold. We prove that a totally umbilical submanifold of a para-Sasakian manifold is invariant. In addition, we investigate curvature properties of such submanifolds and we show that a totally umbilical invariant submanifold of a quasi-conformally flat para-Sasakian manifold is an η-Einstein manifold. Finally, we work on the sectional curvature properties of an invariant submanifold of a quasi-conformally flat para-Sasakian manifold.

AtıfScopus1

İncele

Ünal, İnan

In this study, we consider the N(k)−quasi Einstein manifolds with respect to a type of semi-symmetric metric connection. We suppose that the generator of N(k)−quasi-Einstein manifolds is parallel with respect to semi-symmetric metric connection and we classify such manifolds. In addition, we consider the submanifolds of a N(k)−quasi Einstein manifold and we obtain some conditions on the totally geodesic and the totally umbilic submanifolds. Finally, we consider a para-Kenmotsu space form as an example of N(k)−quasi-Einstein manifolds.

AtıfScopus1

İncele

Sari, Ramazan; Turgut, Aysel; Ünal, İnan

Bu çalışmanın amacı genelleştirilmiş Kenmotsu manifoldları üzerinde concircular eğrilik tensörünün çalışılmasıdır. Concircular düz ve 𝜑-concircular düz genelleştirilmiş Kenmotsu manifoldları incelenmiştir. Ayrıca 𝜑-semi simetrik ve 𝜑-concircular semi simetrik genelleştirilmiş Kenmotsu manifoldları üzerine bazı sonuçlar verilmiştir.

AtıfOpenAlex2·TR Dizin2

İncele

Sari, Ramazan; Ünal, İnan; Aksoy Sari, Elif

Bu çalışmada para Kenmotsu manifoldlaırn skew semi invaryant altmanifoldları çalışıldı. Bir örnek verildive distribüsyonların integrallenebilirlik şartları elde edildi. Para Kenmotsu space formun bu türaltmanifoldları incelendi ve bazı eğrilik özellikleri elde edildi. Son olarak para Kenmotsu manifoldların birtotal geoedezik skew semi invaryant altmanifoldunun 𝜂-Einstein olduğu ispatlandı.

AtıfOpenAlex1·TR Dizin1

İncele