Para-sasakıan manifoldların altmanifoldları
Submanifolds of para-sasakian manifolds
Yazar: BİLAL EFTAL ACET
Danışman: DOÇ. DR. EROL KILIÇ ; YRD. DOÇ. DR. SELCEN YÜKSEL PERKTAŞ
İnönü Üniversitesi / Fen Bilimleri Enstitüsü / Matematik Ana Bilim Dalı
Derece: Doktora, 2014
Konu: Matematik = Mathematics
Dizin: Altmanifold = Submanifold ; Dağıtım = Distribution ; Riemann manifoldu = Riemann manifold ; Vektör alanları = Vector fields ; Vektör demeti = Vector bundle ; Yarı Riemann manifoldu = Semi Riemann manifold

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.

Abstract:
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.