Congruence of Curves in Weyl-Otsuki Spaces

Year 2024, Volume: 14 Issue: 2, 123 - 139, 31.12.2024

Beran Pirinççi

https://doi.org/10.37094/adyujsci.1493094

Abstract

In this paper, we study the congruence of curves in Weyl-Otsuki spaces using Ricci's coefficients of that congruence in the orthogonal case. We first prove that Ricci’s coefficients determine the regular general connection of an Otsuki space. Then, we give the condition for these coefficients in Weyl-Otsuki spaces to be skew-symmetric in the first two indices as in Riemannian spaces. We obtain the necessary and sufficient conditions for the curves of congruence to be geodesic, normal, and irrotational. Finally, we prove that if a congruence satisfies the equation, and any two of the conditions to be geodesic, normal, and irrotational, then it also satisfies the other third one.

Keywords

Weyl-Otsuki Spaces, General Connections, Ricci, Congruence of Curves, Geodesic Curves

Weyl-Otsuki Uzaylarında Kongrüans Eğrileri

Abstract

Bu makalede Weyl-Otsuki uzaylarında kongrüans eğrilerini bu eğrilerin ortogonal olması durumda Ricci katsayılarını kullanarak inceledik. İlk olarak, Ricci katsayılarının bir Otsuki uzayının regüler genel koneksiyonunu belirlediğini gösterdik. Ardından Riemann uzaylarda olduğu gibi Weyl-Otsuki uzaylarında bu katsayıların ilk iki indisine göre ters-simetrik olma koşulunu verdik. Kongrüans eğrilerinin, sırasıyla, jeodezik, normal ve irrotasyonel olması için gerek ve yeter koşulları elde ettik. Son olarak bir kongrüans eğrisinin denklemi ile birlikte jeodezik, normal ve irrotasyonel olma koşullarından herhangi ikisini sağlaması durumunda diğer üçüncü koşulu da sağladığını kanıtladık.

Keywords

Weyl-Otsuki uzayları, Genel koneksiyonlar, Ricci katsayıları, Kongrüans eğrileri, Jeodezik eğriler

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