Yazarlar
Yayınlar
- MakaleAçık Erişim2025Scopus SJRQ4A Classification of N(κ)-contact Metric Manifolds with T-curvature Tensor
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.
AtıfScopus1OpenAlex1
İncele - MakaleAçık Erişim2023On Curvatures of Semi-invariant Submanifolds of Lorentzian Para-Sasakian Manifolds
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.
AtıfOpenAlex1TR Dizin1İncele - MakaleAçık Erişim2020On Quasi-Conformally Flat Para-Sasakian Manifolds
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.
AtıfScopus1İncele - DergiTurkish Journal of Mathematics and Computer Science