Parallel one forms on special Finsler manifolds
Year: 2024
Type: article
Abstract: In this paper, we investigated the existence of parallel 1-forms on specific Finsler manifolds. We demonstrated that Landsberg manifolds admitting a parallel 1-form had a mean Berwald curvature of rank of at most $ n-2 $. As a result, Landsberg surfaces with parallel 1-forms were necessarily Berwaldian. We further established that the metrizability freedom of the geodesic spray for Landsberg metrics with parallel 1-forms was at least $ 2 $. We figured out that some special Finsler metrics did not admit a parallel 1-form. Specifically, no parallel 1-form was admitted for any Finsler metrics of nonvanishing scalar curvature, among them the projectively flat metrics with nonvanishing scalar curvature. Furthermore, neither the general Berwald's metric nor the non-Riemannian spherically symmetric metrics admited a parallel 1-form. Consequently, we observed that certain $ (\alpha, \beta) $-metrics and generalized $ (\alpha, \beta) $-metrics did not admit parallel 1-forms.
Source: AIMS Mathematics
Author: Salah G. Elgendi
Institution: Islamic University of Madinah
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,200
OpenAlex ID: W4405124874