Para-sasakıan manifoldların altmanifoldları
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Dosyalar
Tarih
2014
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Yayıncı
İnönü Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Doktora tezi olarak haz rlanan bu cal sma u c b ol umden olu smaktad r. Birinci b ol um di ger b ol umlerin daha iyi anla s labilmesi i cin temel kavramlara ayr ld . Di ger b ol umler ise tezin orjinal k s mlar d r. Birinci b ol umde yar -Riemann manifoldlar, yar -Riemann manifoldlar n lightlike hipery uzeyleri ve lightlike altmanifoldlar ile birlikte hemen hemen parakontakt manifoldlar ele al nd . _Ikinci b ol umde para-Sasakian manifoldlar n non-dejenere altmanifoldlar cal s ld . Bu b ol umde ilk olarak para-Sasakian manifodlar n invaryant altmanifoldlar n n semiparalel ve 2-semi-paralel olmas i cin gerek ve yeter sartlar elde edildi. Daha sonra bir para-Sasakian manifoldun semi-invaryant altmanifoldlar tan t larak ornekler verildi. Son olarak semi-invaryant altmanifold uzerindeki baz distrib usyonlar n integrallenebilir olma sartlar incelendi. U c unc u b ol um para-Sasakian manifoldlar n lightlike altmanifoldlar na ayr ld . Oncelikle para-Sasakian manifoldlar n lightlike hipery uzeyleri cal s ld . Daha sonra para-Sasakian manifodlar n invaryant ve screen semi-invaryant lightlike hipery uzeyleri tan t larak bu alt manifoldlara ornekler verildi. Ayr ca bir para-Sasakian uzay formun screen semi-invaryant lightlike hipery uzeyleri ile ilgili karekterizasyonlar elde edilidi. Bu b ol umde son olarak para-Sasakian manifoldlar n invaryant, parakontakt CR-lightlike ve radikal transversal lightlike altmanifoldlar incelendi.
This study which is designed as a philosophy doctoral thesis covers three chapters. In the rst chapter, we give some basic concepts such as semi-Riemannian manifolds, the lightlike hypersurfaces and the lightlike submanifolds of semi-Riemannian manifolds, almost paracontact manifolds for the rest of the thesis that readers can easily understand. The other chapters are the original parts of this thesis. In the second chapter, we study non-degenerate submanifolds of para-Sasakian manifolds. Firstly we obtain su cient and necessary conditions for an invariant submanifold of a para-Sasakian manifold to be semi-parallel and 2-semi-parallel, respectively. After we introduce semi-invariant submanifolds of a para-Sasakian manifold and give some examples. Moreover integrability conditions for some distributions on a semi-invariant submanifold of a para-Sasakian manifold are investigated. Third chapter is devoted to the lightlike geometry of para-Sasakian manifolds. In this chapter, we rstly study lightlike hypersurfaces of para-Sasakian manifolds. After we introduce invariant and screen semi-invariant lightlike hypersurfaces of para-Sasakian manifolds and give some examples. Some results for screen semi-invariant lightlike hypersurfaces of a para-Sasakian space form are obtained. In this chapter we nally investigate invariant, paracontact CR-lightlike and radical transversal lightlike submanifolds of para-Sasakian manifolds.
This study which is designed as a philosophy doctoral thesis covers three chapters. In the rst chapter, we give some basic concepts such as semi-Riemannian manifolds, the lightlike hypersurfaces and the lightlike submanifolds of semi-Riemannian manifolds, almost paracontact manifolds for the rest of the thesis that readers can easily understand. The other chapters are the original parts of this thesis. In the second chapter, we study non-degenerate submanifolds of para-Sasakian manifolds. Firstly we obtain su cient and necessary conditions for an invariant submanifold of a para-Sasakian manifold to be semi-parallel and 2-semi-parallel, respectively. After we introduce semi-invariant submanifolds of a para-Sasakian manifold and give some examples. Moreover integrability conditions for some distributions on a semi-invariant submanifold of a para-Sasakian manifold are investigated. Third chapter is devoted to the lightlike geometry of para-Sasakian manifolds. In this chapter, we rstly study lightlike hypersurfaces of para-Sasakian manifolds. After we introduce invariant and screen semi-invariant lightlike hypersurfaces of para-Sasakian manifolds and give some examples. Some results for screen semi-invariant lightlike hypersurfaces of a para-Sasakian space form are obtained. In this chapter we nally investigate invariant, paracontact CR-lightlike and radical transversal lightlike submanifolds of para-Sasakian manifolds.
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Acet, B. E. (2014). Para-sasakıan manifoldların altmanifoldları. İnönü Üniversitesi Fen Bilimleri Enstitüsü. 1-157 ss.
