Hemen hemen değme manifoldlardan Riemann manifoldlar üzerine Riemann submersiyonlar
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Date
2016-05-20
Authors
Beri, Ayşe
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Publisher
Uludağ Üniversitesi
Abstract
Yüksek lisans tezi olarak hazırlanan bu çalışma beş bölümden oluşmaktadır. Birinci bölüm giriş kısmıdır ve bu bölümde konuyla ilgili daha önce yapılan çalışmalardan bahsedilmiştir. İkinci bölümde diğer bölümlerde kullanılacak temel tanım, teorem ve önermeler yer almaktadır. Üçüncü bölümde submersiyonlar çalışılmıştır. Submersiyonun ve Riemann submersiyonun tanımları ve örnekleri verilmiştir. Ayrıca Riemann submersiyonlar için temel denklemler tanımlanmış ve bu denklemlerin özellikleri ile teoremleri verilmiştir. Dördüncü bölümde hemen hemen değme metrik manifoldlar çalışılmıştır. Hemen hemen değme metrik yapı ve hemen hemen manifoldlar incelenmiştir. Özellikle bu tezde çalışılan Kenmotsu manifoldun tanımı ve örnekleri yer almıştır. Beşinci bölüm Kenmotsu manifoldlardan Riemann manifoldlara anti-invariant Riemann submersiyonlar tanıtılıp bu submersiyonların özellikleri araştırılmıştır. Bu bölüm tamamen orijinal sonuçlardan oluşmaktadır.
This study which is designed as master science thesis covers five chapter sections. The first section is the introduction section and in this chapter studies about the subject which were done previously were told of. The second section contains basic definitions, theorems and propositions which will be used in the other sections. In the third section the submersions were studied. Definitions and examples of submersions and Riemannian submersions were given. Also the basic equations for Riemannian submersions were defined and properties of this equations were given. In the fourth section, Almost contact metric manifolds were studied. Almost contact metric structure and almost contact manifolds were examined. Especially the definitions and examples of Kenmotsu manifold which is be studied in this thesis take apart. In the fifth section Anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds were introduced and the properties of this submersions were given. This section contains completely the original studies.
This study which is designed as master science thesis covers five chapter sections. The first section is the introduction section and in this chapter studies about the subject which were done previously were told of. The second section contains basic definitions, theorems and propositions which will be used in the other sections. In the third section the submersions were studied. Definitions and examples of submersions and Riemannian submersions were given. Also the basic equations for Riemannian submersions were defined and properties of this equations were given. In the fourth section, Almost contact metric manifolds were studied. Almost contact metric structure and almost contact manifolds were examined. Especially the definitions and examples of Kenmotsu manifold which is be studied in this thesis take apart. In the fifth section Anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds were introduced and the properties of this submersions were given. This section contains completely the original studies.
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Keywords
Riemannian submersiyon, Konformal submersiyon, Katlı çarpım, Kenmotsu manifold, Anti-invariant submersiyon, Riemannian submersions, Conformal submersions, Warped product, Kenmotsu manifolds, Anti-invariant submersions
Citation
Beri, A. (2016). Hemen hemen değme manifoldlardan Riemann manifoldlar üzerine Riemann submersiyonlar. Yayınlanmamış yüksek lisans tezi. Uludağ Üniversitesi Fen Bilimleri Enstitüsü.