Generalized Quasi-Conformal Curvature Tensor On Normal Metric Contact Pairs

Abstract

The aim of this paper is to examine normal metric contact pair (NMCP) manifolds under the flatness conditions on
generalized quasi-conformal (GQC) curvature tensor. It is interested to classify GQC-flat and GQC-Z-flat NMCP
manifolds. We prove that a GQC-flat NMCP manifold is a generalized quasi-Einstein (GQE) manifold and also, such
manifolds are the space of generalized quasi-constant curvature. Finally, we consider the sectional curvature of NMCP
manifolds under the flatness conditions of GQC curvature tensor.

Keywords

• Contact metric pair
• generalized quasi-conformal curvature tensor
• curvature properties

Kontakt Metrik Çiftler Üzerinde Genelleştirilmiş Quasi-Conformal Eğrilik Tensörü

Abstract

Bu çalışmanın amacı, normal metrik kontakt çift (NMCP) manifoldlarını genelleştirilmiş quasi-conformal eğrilik
(GQC) tensörünün sıfırlık koşulları altında incelemektir. Bu kapsamda GQC-düz ve GQC-Z-düz NMCP manifoldları ile
ilgilenilmiştir. Bir GQC-düz manifoldun genelleştirilmiş yarı-Einstein (GQE) manifold olduğu ve bu çeşit manifoldların
genelleştirilmiş yarı-sabit eğriliğe sahip olduğu ispatlanmıştır. Son olarak, GQC eğrilik tensörünün düzlük şartları altında,
NMCP manifoldlarının kesitsel eğrilikleri ele alınmıştır.

Keywords

• Kontakt metrik çift,
• eğrilik özellikleri,
• genelleştirilmiş quasi-conformal eğrilik tensörü

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