Analysis of Total Umbilical Fibers in Riemannian Submersions with Quarter Symmetric Non-Metric Connections

Year 2025, Volume: 11 Issue: 1, 30 - 55, 30.06.2025

Esra Karataş , Semra Zeren , Mustafa Altın

https://doi.org/10.29132/ijpas.1523117

https://izlik.org/JA98MM55LA

Abstract

In this study, we examine the geometric properties of Riemannian submersions with quarter symmetric non-metric connections. Our work provides a compre-hensive analysis of the Weyl projective curvature tensor, the concircular curvature tensor, and the conharmonic curvature tensor. We also investigate how these curvature tensors interact with the total umbilic fibers, particularly focusing on their behavior when such fibers are present in Riemannian submersions. First we introduce basic properties of quarter symmetric non-metric connections. Subse-quently, we compute the relevant curvature tensors and analyze their interplay with total umbilic fibers. In this context, we elucidate relationships between var-ious curvature tensors and certain geometric properties, as well as the effects of these relationships on Riemannian submersions.

Keywords

Curvature tensors , quarter symmetric non-metric connection , Riemannian manifold , Riemannian submersion

Quarter-Simetrik Non-Metrik Konneksiyonlu Riemann Submersiyonlarda Total Umbilik Liflerin Analizi

https://izlik.org/JA98MM55LA

Abstract

Bu çalışmada quarter simetrik non-metrik konneksiyona sahip Riemann sub-mersiyonların geometrik özellikleri incelenmektedir. Çalışma, Weyl projektif eğrilik tensörü, koncircular eğrilik tensörü ve konharmonic eğrilik tensorlerine ilişkin kapsamlı bir analiz sunmaktadır. Ayrıca bu eğrilik tensörlerinin total um-bilik lifler üzerindeki etkileşimleri de araştırılmaktadır. Ek olarak söz konusu tensörlerin Riemann submersiyonlarında total umbilik liflerinin varlığı du-ru-munda ortaya çıkan yapısal özellikleri de ele alınmaktadır. İlk olarak, quarter simetrik non-metrik konneksiyonların tanımı ve temel özellikleri incelenmekte, sonrasında bu konneksiyonların Riemann submersiyonları üzerindeki etkileri incelenmektedir. Eğrilik tensörleri hesaplanarak total umbilik liflerle etkileşim-leri analiz edilmektedir. Bu bağlamda, farklı eğrilik tensörlerinin ge-ometrik özel-liklerinin birbiri ile ilişkisi ve Riemann submersiyonları üzerindeki etkileri ortaya konulmaktadır.

Keywords

Eğrilik tensörleri , quarter simetrik non-metrik konneksiyon , Riemann manifoldu , Riemann submersiyonu

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