ON KÂHLER-EINSTEIN METRIC

Abstract

In this study, we were mentioned Kâhler-Einstein metrics and the first Chern class of the Chern classes which is the characteristic class of complex vector bundles with a orientation and used to distinguish the differences between two manifolds. Relation between Kâhler-Einstein metrics and first Chern class was mentioned. Positive case of the first Chern class which has positive, negative and zero was examined and for this case how to find Kâhler-Einstein metrics was explained.

Keywords

• Kâhler-Einstein Metrics,First Chern Class,Futaki Invaryant

KÂHLER-EİNSTEİN METRİK ÜZERİNE

Abstract

Bu çalışmada iki manifold arasındaki farklılıkları ayırt etmek için kullanılan ve bir yönlendirmeye sahip kompleks vektör demetlerinin karakteristik sınıfı olan Chern sınıflarından birinci Chern sınıfı ve Kâhler-Einstein metriklerine değinilmiş aynı zamanda da aralarındaki ilişkiden bahsedilmiştir. Birinci Chern sınıfının pozitif, negatif ve sıfır olduğu durumlardan pozitif olduğu durum incelenmiş ve bu durum için Kâhler-Einstein metriklerinin nasıl bulunabileceği açıklanmıştır.

 

Keywords

• Kâhler-Einstein Metrik,Birinci Chern Sınıfı,Futaki İnvaryantı

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