Lightlike hiperyüzeylerın geometrisi
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Dosyalar
Tarih
2013
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
İnönü Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tez lightlike hiperyüzler ile ilgili yapılan çalısmaların bir derlemesi olarak dört bölümden meydana gelmistir.Birinci bölüm giris olarak düzenlenmistir. Ikinci bölümde, diger bölümlere faydalı olacak temel tanım ve kavramlar; vektör demetleri ve distribüsyonlar, semi-Riemann manifoldlar, semi-Riemann manifoldların lightlike altmanifoldları ve lightlike manifoldlar ele alınmıstır. Üçüncü bölümde lightlike hiperyüzeyler ve lightlike hiperyüzeylerle ilgili tanım ve teoremler verilerek ekran konformal hiperyüzeyler incelendi, ekran distribüsyonunun tekligi arastırıldı ve bir tek ekran distribüsyonunundaki temel sonuçlar bulunmustur. Ayrıca bir semi-Riemann manifoldunun bir lightlike hiperyüzeyinin yeni bir kavramı olan Indirgenmis skalar egriligi incelenmistir. Dördüncü bölümde lightlike Einstein hiperyüzeyler tanıtılarak üzerindeki distribüsyonların geometrisi incelenmistir. Ayrıca, R^(n+2)q semi-Öklidyen uzayının bir lightlike hiperyüzeyi için Gauss denklemi verilmistir. Sonra Minkowski spacetime?ın her ekran konformal hiperyüzeyinin semi-simetrik oldugu gösterilmistir. Daha sonra, ekran konformal lightlike hiperyüzeyin semi-simetrik olma kosulu ile ekran distribüsyonunun semi-simetrik olması kosulu arasında açık bir iliski oldugu vurgulanmıstır. Ayrıca semi-Öklidyen uzayların Ricci semi-simetrik lightlike hiperyüzeyleri ve bunlardan elde edilen bir sart altında total geodezikligi ele alınmıs ve bir Lorentzian manifoldun paralel lightlike hiperyüzeyler üzerinde bir karekterisazyonu verilmistir.
This thesis consists of four chapter.The first chapter has been designed as an introduction.The second chapter is devoted to the basic materials such as vector bundles, distributions, semi-Riemannian manifolds, lightlike submanifolds of semi-Riemannian manifold and lightlike manifolds, which will be useful for other chapters. In the third chapter, lightlike hypersurfaces have been introduced and theorems about lightlike hypersurfaces have been given. After investigating unique existence of screen distributions, it was found basic results on unique existence of screen distributions. Besides, the induced scalar curvature which is a new concept is examined in a lightlike hypersurface of a semi-Riemanian manifold. In the fourth chapter, we introduced lightlike Einstein hypersurfaces and the geometry of distributions is investigated on the lightlike Einstein hypersurfaces. Besides, Gauss equation for lightlike hypersurface of a semi-Euclidean space has been given. Then, we obtained that every screen conformal lightlike hypersurface of the Minkowski spacetime is semi-symmetric. We showed that the semi-symmetry condition of a screen conformal lightlike hypersurface reduced to the semi-symmetry condition of a leaf of its screen distribütion. We also obtained that semi-symmetric and Ricci semi-symmetric lightlike hypersurfaces are totally geodesic under certain conditions. Morever, we showed that there exist no non-totally geodesic parallel hypersurfaces in a Lorentzian space.
This thesis consists of four chapter.The first chapter has been designed as an introduction.The second chapter is devoted to the basic materials such as vector bundles, distributions, semi-Riemannian manifolds, lightlike submanifolds of semi-Riemannian manifold and lightlike manifolds, which will be useful for other chapters. In the third chapter, lightlike hypersurfaces have been introduced and theorems about lightlike hypersurfaces have been given. After investigating unique existence of screen distributions, it was found basic results on unique existence of screen distributions. Besides, the induced scalar curvature which is a new concept is examined in a lightlike hypersurface of a semi-Riemanian manifold. In the fourth chapter, we introduced lightlike Einstein hypersurfaces and the geometry of distributions is investigated on the lightlike Einstein hypersurfaces. Besides, Gauss equation for lightlike hypersurface of a semi-Euclidean space has been given. Then, we obtained that every screen conformal lightlike hypersurface of the Minkowski spacetime is semi-symmetric. We showed that the semi-symmetry condition of a screen conformal lightlike hypersurface reduced to the semi-symmetry condition of a leaf of its screen distribütion. We also obtained that semi-symmetric and Ricci semi-symmetric lightlike hypersurfaces are totally geodesic under certain conditions. Morever, we showed that there exist no non-totally geodesic parallel hypersurfaces in a Lorentzian space.
Açıklama
Anahtar Kelimeler
Semi-Riemann manifold, Lightlike manifold, Lightlike hiperyüzey, Ekran konformal hiperyüzey, Lightlike Einstain hiperyüzey, İndirgenmiş eğrilik, Total geodezik, Total umbilik, Semi-simetrik metrik konneksiyon, Ricci eğrilik tensörü, Lightlike hypersurface, Screen conformal hypersurface, Lightlike Einstain hypersurface, Induced scalar curvature, Totally geodesic, Totally umbilical, Semi-symmetry metric connection, Ricci curvature tensor
Kaynak
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Polat, M. (2013). Lightlike hiperyüzeylerın geometrisi. İnönü Üniversitesi Fen Bilimleri Enstitüsü. 1-87 ss.