Lightlike alt manifoldlar üzerinde ricci solitonlar
Küçük Resim Yok
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
İnönü Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Doktora tezi olarak hazırlanan bu çalışma dört bölümden oluşmaktadır. Giriş olarak verilen birinci bölümde, Ricci solitonlarla ilgili literatür bilgisi ve tezin genel içerigi hakkında kısa ? bilgiler verilmiştir. İkinci bölümde ise, tezin anlaşılabilir olması için yarı-Riemann manifoldlar, altmanifoldlar ve yarı-Riemann manifoldların lightlike altmanifoldları ile ilgili temel kavramlar verildi. Üçüncü bölümde, ilk olarak bir yarı-Riemann manifoldun lightlike hiperyüzeyi üzerinde Ricci solitonlar, Rigged metrik yardımıyla incelendi ve bu bölümde potansiyel vektör alanı concurrent vektör alanı ve concircular vektör alanı olarak alınarak, lightlike hiperyüzeyler üzerinde Ricci solitonların var olması için gerek ve yeter ¸sartlar ile karekterizasyon teoremleri elde edildi. Son bölüm olan dördüncü bölümde ise lightlike altmanifoldlar üzerinde Ricci solitonlar en genel haliyle çalışıldı. Bu bölümde ilk önce ek boyutu iki olan half lightlike ve coisotropic altmanifoldlar üzerinde Ricci solitonlar çalışıldı ve potansiyel vektör alanları özel vektör alanları olarak alınarak karekterizasyonlar verildi. Bu son bölümde en son olarak r?lightlike altmanifoldlar üzerinde Ricci solitonlar incelendi ve potansiyel vektör alanlarının özel vektör alanları (concurrent, concircular, v.s.) olması durumunda karekterizasyonlar verildi.
This study, prepared as a doctoral thesis, consists of four chapters. In the first chapter, which is given as an introduction, brief information about the literature on Ricci solitons and the general content of the thesis is given. In the second chapter, basic concepts about semi-Riemann manifolds, submanifolds and lightlike submanifolds of semi-Riemann manifolds are given to make the thesis understandable. In the third chapter, firstly, Ricci solitons on the lightlike hypersurface of a semi-Riemann manifold were examined with the help of the Rigged metric, and in this chapter, the potential vector field was taken as concurrent vector field and concircular vector field, and the necessary and sufficient conditions and characterizations were given for the existence of Ricci solitons on lightlike hypersurfaces and some theorems and results were obtained. In the last chapter, the fourth chapter, Ricci solitons were studied in their most general form on lightlike submanifolds. In this section, first Ricci solitons were studied on half lightlike and coisotropic submanifolds with additional dimension two, and characterizations were given by taking potential vector fields as special vector fields. In this last section, Ricci solitons on r-lightlike submanifolds were examined and characterizations were given in case potential vector fields are special vector fields (concurrent, concircular, etc.).
This study, prepared as a doctoral thesis, consists of four chapters. In the first chapter, which is given as an introduction, brief information about the literature on Ricci solitons and the general content of the thesis is given. In the second chapter, basic concepts about semi-Riemann manifolds, submanifolds and lightlike submanifolds of semi-Riemann manifolds are given to make the thesis understandable. In the third chapter, firstly, Ricci solitons on the lightlike hypersurface of a semi-Riemann manifold were examined with the help of the Rigged metric, and in this chapter, the potential vector field was taken as concurrent vector field and concircular vector field, and the necessary and sufficient conditions and characterizations were given for the existence of Ricci solitons on lightlike hypersurfaces and some theorems and results were obtained. In the last chapter, the fourth chapter, Ricci solitons were studied in their most general form on lightlike submanifolds. In this section, first Ricci solitons were studied on half lightlike and coisotropic submanifolds with additional dimension two, and characterizations were given by taking potential vector fields as special vector fields. In this last section, Ricci solitons on r-lightlike submanifolds were examined and characterizations were given in case potential vector fields are special vector fields (concurrent, concircular, etc.).
Açıklama
Anahtar Kelimeler
Matematik, Mathematics
