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.

İncele

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

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

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

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