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.

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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

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.

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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.

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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.

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