SavedAdd your journal

Journals / Dumlupınar Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2019 / Cilt: 0 - Sayı: 43

ON KÂHLER-EINSTEIN METRIC

KÂHLER-EİNSTEİN METRİK ÜZERİNE

Cemile YETİM
Mine TURAN
Pages
91–107
Publication Date
2022-10-11
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data:Relation between Kâhler-Einstein metrics and first Chern class was mentioned.
💡
Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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.

Özet

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

🔖

Cite This Article

YETİM, C., TURAN, M. (2022). ON KÂHLER-EINSTEIN METRIC. Dumlupınar Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 0 - Sayı: 43, 91–107. https://ajindex.com/articles/492306

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (21)

  1. Pragacz, P., (2012), Characteristic Classes with Applications yo Geometry, Topology and Number Theory, Instytut Matematyczny Polskiej Akademii Nauk, Poland
  2. Ozan, Y., (2016), Türevlenebilir Manifoldlara Giriş, ODTÜ, Ankara
  3. Hatcher, A., (2002), Algebraic Topology, Cambridge University Press, England
  4. Szekelyhidi, G., (2013), Introduction to Extremal metrics Preliminary Version
  5. Faulk, M., (2016), First Chern Classes of Kahler Manifolds, Columbia University, New York
  6. Fine, J., (2012), A rapid introduction to Kähler geometry, Chapter 2: Holomorphic line bundles, preprints, Université Libre de Bruxelles, Belgique
  7. Santoro, B., (2009), Introduction to Evolution Equations in Geometry, Nacional de Matematica Pura e Aplicada-IMPA, Rio de Janeiro, Brazil
  8. Li, C., (2012), Kahler-Einstein Metrics and K-Stability, PhD thesis, Princeton University
  9. Moroianu, A., (2007), Lectures on Kahler Geometry, Cambridge University Press, Paris
  10. Tian, G., (2000), Kahler-Einstein Manifolds of Positive Scalar Curvature, İnternational Press
  11. Wang, X. J., Zhu, X., (2004), Kahler-Ricci solitons on toric manifolds with positive first Chern class, Advances in Mathematics 188, 87-103
  12. Spotti, C., (2016), Compact moduli spaces of Kahler-Einstein Fano varieties, Cambridge of University, England
  13. Bando, S., Mabuchi, T., (1987), Uniqueness of Einstein Kahler metrics modulo connected group actions, Algebraic Geometry, Adv. Studies in Pure Math., 10
  14. Tian, G., (2014), Kahler-Einstein metrics on Fano manifolds, Japanese Journal of Mathematics, Volume 10, Issue 1, pp 1–41
  15. Tian, G., (1990), Kahler-Einstein on algebraic manifolds, Proceedings of the International Congress of Mathematicians, Vol. I, II,587-598, Math. Soc. Japan, Tokyo, 1991
  16. Tsuboi, K., (2009), On the existence of Kahler metrics of constant scalar curvature, Tohoku Math. J., vol. 61(2), 241-252
  17. Tian, G., (1991), Lectures on Einstein Manifolds: Kahler-Einstein Manifolds and Positive Scalar Curvature, Mathematics Subject Classification. Primary 53C20, İnternational Press
  18. Tian, G., (1997), Kahler-Einstein metrics with positive scalar curvature. Invent. Math., 130, 1- 39
  19. Matsushima, Y., (1957), Sur la structure du group homeomorphismes analytiques d’une certain variete, Kaehlerienne, Nagoya Math. J., 11, 145-150
  20. Futaki, A., (1983), An obstruction to the existence of Kahler-Einstein metrics, Inv. Math., 73, 437-443
  21. Stoppa, J., (2009),