On Twisted Products Finsler Manifolds

TL;DR

This paper investigates the geometric properties of twisted product Finsler manifolds, focusing on curvature characteristics and dual flatness, by extending Finsler metrics from two base manifolds and analyzing their combined structure.

Contribution

It introduces the concept of twisted product Finsler manifolds, explores their curvature properties, and examines conditions for dual flatness, extending existing Finsler geometric frameworks.

Findings

Derived expressions for Riemannian and non-Riemannian curvatures of twisted product Finsler manifolds.

Established relations between curvatures of the product and those of the component manifolds.

Analyzed conditions for local dual flatness in twisted product Finsler manifolds.

Abstract

On the product of two Finsler manifolds M1 M2, we consider the twisted metric F which is construct by using Finsler metrics F1 and F2 on the manifolds M1 and M2, respectively. We introduce horizontal and vertical distributions on twisted product Finsler manifold and study Creducible and semi-C-reducible properties of this manifold. Then we obtain the Riemannian curvature and some of non-Riemannian curvatures of the twisted product Finsler manifold such as Berwald curvature, mean Berwald curvature and we find the relations between these objects and their corresponding objects on M1 and M2. Finally, we study locally dually flat twisted product Finsler manifold.