Kompleks geometride Riemann dönüşümler üzerine
Küçük Resim Yok
Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
İnönü Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Yüksek lisans tezi olarak hazırlanan bu çalışma beş bölümden oluşmaktadır. Birinci bölümde, konunun tarihsel gelişimi ve bu tezde ele alınan problemlerin tanıtımı yapılmaktadır. İkinci bölümde diğer bölümlerde faydalı olacak temel tanım, teorem ve kavramlar ele alınmaktadır. Üçüncü bölümde, kompleks geometride invaryant ve anti-invaryant Riemann dönüşümler çalışılmaktadır. Bu başlık altında önce hemen hemen Hermityen manifoldlardan Riemann manifoldlara tanımlanan invaryant Riemann dönüşümler tanımlanıp, bu dönüşümün varlığı ile ilgili bir örnek verilmiştir. Daha sonra, hemen hemen Hermityen manifoldlardan Riemann manifoldlara tanımlanan anti-invaryant Riemann dönüşümler tanımlanıp, bu dönüşümün varlığı ile ilgili örnek verilmiştir. Son olarak, bu dönüşümler için distribüsyonların paralelliği ve tamamen geodezik olma durumları incelenmiştir. Dördüncü bölümde, kompleks geometride, hemen hemen Hermityen manifoldlardan Riemann manifoldlara tanımlanan yarı-invaryant Riemann dönüşümler çalışılmıştır. Bu başlık altında hemen hemen Hermityen manifoldlardan Riemann manifoldlara tanımlanan yarı-invaryant Riemann dönüşümler tanıtılıp, bu dönüşümün varlığı ile ilgili örnek verilmiştir. Daha sonra, bu dönüşümler için distribüsyonların integrallenebilirliği ve paralelliği incelenmiştir. Son olarak tamamen umbilik noktalar ile yarı-invaryant Riemann dönüşümler incelenmiş ve genel bir sonuç elde edilmiştir. Son bölüm olan beşinci bölümde, kompleks geometride, hemen hemen Hermityen manifoldlardan Riemann manifoldlara tanımlanan slant-Riemann dönüşümler çalışılmıştır. Bu başlık altında ilk olarak hemen hemen Hermityen manifoldlardan Riemann manifoldlara tanımlanan slant-Riemann dönüşümler tanıtılıp bu dönüşümün varlığı ile ilgili örnek verilmiştir. Daha sonra slant-Riemann dönüşüm olma şartları, harmonik olma durumu, paralelliği ve tamamen geodezik olma durumu incelenip genel bir ayrışım teoremi verilmiştir.
This study, which was prepared as a master's thesis, consists of five chapters. In the first chapter, the historical development of the subject and the problems discussed in this thesis are introduced. In the second part, basic definitions, theorems and concepts that will be useful in other parts are discussed. In the third chapter, invariant and anti-invariant Riemannian maps in complex geometry are studied. Under this title, invariant Riemannian maps, which are defined Riemannian manifolds from almost Hermitian manifolds, are defined and an example of the existence of this map is given. Then, anti-invariant Riemannian maps, which are defined Riemannian manifolds from almost Hermitian manifolds, are defined and an example of the existence of this maps is given. Finally, the parallel of the distributions and their being completely geodesic were investigated for these maps. In the fourth chapter, semi-invariant Riemannian maps defined Riemannian manifolds from almost Hermitian manifolds in complex geometry are studied. Under this title, semi-invariant Riemann maps defined Riemannian manifolds from almost Hermitian manifolds are introduced and an example of the existence of this map is given. Then, the integrability and parallelism of the distributions for these maps are examined. Finally, fully umbilical points and semi-invariant Riemannian maps were examined and a general result was obtained. In the fifth chapter, which is the last chapter, slant-Riemann maps defined Riemannian manifolds from almost Hermitian manifolds in complex geometry are studied. Under this title, firstly, slant-Riemannian maps, which are defined Riemannian manifolds from almost Hermitian manifolds, are introduced and an example of the existence of this map is given. Then, the conditions of being slant-Riemannian maps, being harmonic, paralell and being completely geodesic were examined and a general decomposition theorem was given.
This study, which was prepared as a master's thesis, consists of five chapters. In the first chapter, the historical development of the subject and the problems discussed in this thesis are introduced. In the second part, basic definitions, theorems and concepts that will be useful in other parts are discussed. In the third chapter, invariant and anti-invariant Riemannian maps in complex geometry are studied. Under this title, invariant Riemannian maps, which are defined Riemannian manifolds from almost Hermitian manifolds, are defined and an example of the existence of this map is given. Then, anti-invariant Riemannian maps, which are defined Riemannian manifolds from almost Hermitian manifolds, are defined and an example of the existence of this maps is given. Finally, the parallel of the distributions and their being completely geodesic were investigated for these maps. In the fourth chapter, semi-invariant Riemannian maps defined Riemannian manifolds from almost Hermitian manifolds in complex geometry are studied. Under this title, semi-invariant Riemann maps defined Riemannian manifolds from almost Hermitian manifolds are introduced and an example of the existence of this map is given. Then, the integrability and parallelism of the distributions for these maps are examined. Finally, fully umbilical points and semi-invariant Riemannian maps were examined and a general result was obtained. In the fifth chapter, which is the last chapter, slant-Riemann maps defined Riemannian manifolds from almost Hermitian manifolds in complex geometry are studied. Under this title, firstly, slant-Riemannian maps, which are defined Riemannian manifolds from almost Hermitian manifolds, are introduced and an example of the existence of this map is given. Then, the conditions of being slant-Riemannian maps, being harmonic, paralell and being completely geodesic were examined and a general decomposition theorem was given.
Açıklama
Anahtar Kelimeler
Matematik, Mathematics
