5 Boyutta Kuasi-para-Sasaki Yapılar Üzerine

Abstract

Bu çalışmada 5 boyutlu nilpotent Lie cebirleri üzerinde kuasi-para-Sasaki yapıların varlığı incelenmiştir. Birbirine izomorf olmayan altı tane Abelyen olmayan nilpotent Lie cebri vardır. Kuasi-para-Sasaki yapıların bu Lie cebirlerinden sadece birinde olduğu gösterilmiştir. Kuasi-para-Sasaki yapılar hemen-hemen parakontak metrik yapıların sınıflandırılmasına göre G_5+G_8 sınıfına karşılık gelmektedir. 5 boyutlu nilpotent bir Lie cebri üzerinde kuasi-para-Sasaki bir yapının G_5 veya G_8 sınıfından olduğu kanıtlanmıştır.

Keywords

• Hemen-hemen Parakontak Metrik Yapı
• 5-boyutlu Nilpotent Lie Cebri
• Kuasi-para-Sasaki Yapı

On Quasi-para-Sasakian Structures on 5-dimensions

Abstract

In this study, we investigate the existence of quasi-para-Sasakian structures on five dimensional nilpotent Lie algebras. There are six non-abelian nilpotent Lie algebras. We show that quasi-para-Sasakian structures exist only on one of these algebras. Quasi-para-Sasakian structures correspond to the class G_5+G_8 in the classification of almost paracontact metric structures. We show that a quasi-para-Sasakian structure on a five dimensional nilpotent Lie algebra is either in G_5 or G_8.

Keywords

• Almost Paracontact Metric Structure
• 5-dimensional Nilpotent Lie Algebra
• Quasi-para-Sasakian Structure

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