Almost Product Lorentzian Walker Üç-Manifoldu Üzerinde İkiz Metriğin Ricci Geometrisi

Öz

Bu çalışmada, almost product Lorentzian Walker üç-manifold (M^3,J,g_f ) üzerinde tanımlı ikiz metrik G_f ile ilişkili Ricci tensörünün geometrisine dair çeşitli teoremler ve sonuçlar sunulmaktadır. Öncelikle, (M^3,J,g_f,G_f) dörtlüsünün Ricci flat olması için gerekli ve yeterli koşullar elde edilmekte, ardından manifoldun Ricci flatliği ile flatliği arasındaki ilişki incelenmektedir. Buna ek olarak, söz konusu (M^3,J,g_f,G_f) dörtlüsünün yerel Ricci simetrik ve döngüsel paralel Ricci olmasına ilişkin gerekli ve yeterli koşulları veren bir teorem ailesi ortaya konulmaktadır. Bu teoremlerin bir sonucu olarak, bu iki geometrik manifold sınıfı arasındaki içsel ilişki açık bir biçimde karakterize edilmektedir.

Anahtar Kelimeler

• Walker Manifoldları
• Almost Product Yapı
• Ricci Tensör
• Yerel Ricci simetrik manifoldlar
• Döngüsel paralel Ricci manifoldlar

Destekleyen Kurum

Bu çalışma herhangi bir kurum veya kuruluş tarafından desteklenmemiştir.

Etik Beyan

Bu çalışma, insan veya hayvan denekleri içermediğinden etik kurul izni gerektirmemektedir.

Teşekkür

Yazar, son derece değerli yorum ve önerilerinden dolayı Prof. Aydın Gezer’e içten teşekkürlerini sunar.

Ricci Geometry of Twin Metric on Almost Product Lorentzian Walker Three-Manifold

Öz

In this study, several theorems and results concerning the geometry of the Ricci tensor associated with a twin metric G_f on an almost product Lorentzian Walker three-manifold (M^3,J,g_f ) are presented. Firstly, we constitute the necessary and sufficient condition under which the quadruple (M^3,J,g_f,G_f) is Ricci-flat, and subsequently examine the relationship between the Ricci-flatness and flatness of the manifold. Furthermore, we establish a collection of theorems describing the conditions under which the quadruple (M^3,J,g_f,G_f) is locally Ricci symmetric and cyclic parallel Ricci. As a consequence of these theorems, the intrinsic relationship between these two geometric classes of manifolds is explicitly characterized.

Anahtar Kelimeler

• Walker Manifolds
• Almost Product Structure
• Ricci Tensor
• Locally Ricci Symmetric Manifolds
• Cyclic Parallel Ricci Manifolds

Destekleyen Kurum

This study was not supported by any institution or organization.

Etik Beyan

This study does not involve human or animal subjects and therefore does not require ethical approval.

Teşekkür

The author is deeply grateful to Prof. Aydın Gezer for his highly valuable comments and suggestions.

Kaynakça

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