2025/10/26 by Soleiman, A., Taha, Ebtsam H.
#53B40 #53C60 #58B20 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2510.22463
We explore a generalization of Matsumoto metric intrinsically. Given a Finsler manifold (M,F) which admits a concurrent π-vector field φ, we consider the change \widehatF(x,y)=\frac F2 (x,y) F(x,y)-Φ(x,y), where Φ is the associated concurrent π-form with F(x,y) > Φ(x,y) for all (x,y) ∈ \T M. We find the condition under which the generalized ϕ-Matsumoto metric \widehatF is a Finsler metric. Moreover, the relations between the associated Finslerian geometric objects of \widehatF and F are obtained, namely, the relations between angular metric tensors, metric tensors, Cartan torsions, geodesic sprays, Barthel connections (along with its curvature) and Berwald connections. Further, we prove that the Finsler metrics F and \widehatF can never be projectively related. Also, a condition for the π-vector field φ to be concurrent with respect to \widehatF is acquired. Moreover, an example of a rational Finsler metric admitting a concurrent π-vector field together with the associated change \widehatF is provided. Finally, we find the conditions that preserve the almost rationality property of a Finsler metric F under the ϕ-Matsumoto change.