Quarter simetrik konneksiyonlu Semi-Riemann manifoldların lightlike altmanifoldları
Yükleniyor...
Dosyalar
Tarih
2012
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
İnönü Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Tez bes bölümden olusmaktadır. Birinci bölüm; Riemann manifoldları, c¸arpım manifoldları, Lightlike hipery¨uzeyler ve altmanifoldlar, quarter, semi-simetrik non metrik konneksiyonlar ve kompleks altmanifoldlarla ilgili temel kavramlardan ibaretdir. Diğer bölümler çalısmanın orjinal kısımlarıdır. İkinci bölümde bir semi-Riemannian çarpım manifoldunun lightlike hiperyüzeyleri incelendi.İlk önce lightlike hiperyüzeyler, F- çarpım yapısından yararlanarak sınflandırıldı (screen semi-invaryant, radikal antiinvaryant, screen invaryant) ve bu tip hiperyüzeylerle ilgili sonuçlar verildi. Daha sonra ise F- çarpım yapısı yardımı ile elde edilen quarter simetrik non-metrik konneksiyona göre bu tip lightlike hiperyüzeylerin geometrisi gözönune alındı. Üçüncü bölümde ise Half-lightlike altmanifoldların yeni bir tipi (semi-invaryant) tanımlandı ve bu altmanifoldlar ilk ¨once Levi-Civita konneksiyonu ve indirgenmis konneksiyona göre gözönüne alındı. Daha sonra bu altmanifoldlar quarter simetrik non-metrik konneksiyona göre incelendi. Dördüncü bölümde semi-Riemann çarpım manifoldunun coisotropic ve r- lightlike altmanifoldlarının Levi-Civita ve quarter simetrik non-metrik konneksiyona göre bazı özellikleri irdelendi. Beşinci bölümde ise belirsiz Kaehler manifoldların semi-invaryant Lightlike altmanifoldları Levi-Civita ve quarter simetrik non-metrik konneksiyona göre incelendi.
This thesis consists of five chapters. The first chapter deals with the basic concepts of Riemann manifolds, product manifolds, lightlike hipersurface and submanifolds, quarter, semi-symmetric non-metric connections and complex submanifolds. Other chapters are the parts of original study. In the second chapter, lightlike hipersurface of a semi-Riemannian product manifold was investigated. Firstly ightlike hipersurfaces were classified, with the help of $F-$ product structure (screen semi-invariant, radical anti-invariant, screen invariant) and the results of this type of hipersurfaces were given. Later, the geometry of this type of lightlike hypersurfaces was considered with respect to quarter symmetric non-metric connection, which was obtained with the help of $F-$ product structure. In the third chapter, a new type of half-lightlike submanifolds (semi-invariant) was defined and first of all, these submanifolds were considered according to the Levi-Civita connection and induced connection. Subsecuently these submanifolds were investigated with respect to quarter symmetric non-metric connection. In the fourth chapter, some characteristics of coisotropic and $r-$ lightlike submanifolds of semi-Riemannian product manifold were evaluated with respect to Levi-Civita and quarter-symmetric non-metric connection. In the fifth chapter, semi-invariant lightlike submanifolds of indefinite Kaehler manifolds were examined with respect to Levi-Civita and quarter-symmetric non-metric connection.
This thesis consists of five chapters. The first chapter deals with the basic concepts of Riemann manifolds, product manifolds, lightlike hipersurface and submanifolds, quarter, semi-symmetric non-metric connections and complex submanifolds. Other chapters are the parts of original study. In the second chapter, lightlike hipersurface of a semi-Riemannian product manifold was investigated. Firstly ightlike hipersurfaces were classified, with the help of $F-$ product structure (screen semi-invariant, radical anti-invariant, screen invariant) and the results of this type of hipersurfaces were given. Later, the geometry of this type of lightlike hypersurfaces was considered with respect to quarter symmetric non-metric connection, which was obtained with the help of $F-$ product structure. In the third chapter, a new type of half-lightlike submanifolds (semi-invariant) was defined and first of all, these submanifolds were considered according to the Levi-Civita connection and induced connection. Subsecuently these submanifolds were investigated with respect to quarter symmetric non-metric connection. In the fourth chapter, some characteristics of coisotropic and $r-$ lightlike submanifolds of semi-Riemannian product manifold were evaluated with respect to Levi-Civita and quarter-symmetric non-metric connection. In the fifth chapter, semi-invariant lightlike submanifolds of indefinite Kaehler manifolds were examined with respect to Levi-Civita and quarter-symmetric non-metric connection.
Açıklama
Anahtar Kelimeler
Quarter Simetrik Non-metrik Konneksiyon, Lightlike Hiperyüzey, Half-lightlike Altmanifold, Lightlike Altmanifold, Semi-Riemann Çarpım Manifoldu, Coisotropic Altmanifold, Screen invaryant Altmanifold, Radikal anti-invaryant Altmanifold, Semi-invaryant Altmanifold, Quarter Symmetric Non-metric connection, Lightlike Hipersurface, Half-lightlike submanifold, Lightlike submanifold, Semi-Riemann product Manifold, Coisotropic submanifold, Screen invariant submanifold, Radical anti-invariant submanifold,, Semi-invariant submanifold
Kaynak
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Bahadır, O. (2012). Quarter simetrik konneksiyonlu Semi-Riemann manifoldların lightlike altmanifoldları. İnönü Üniversitesi Fen Bilimleri Enstitüsü. 1-139 ss.
