Finite Volume Einstein Finsler Warped Product Manifolds of Non-positive or Non-negative Scalar Curvature

TL;DR

This paper explores the extension of warped product constructions to Finsler manifolds, particularly in the context of Einstein metrics with non-positive or non-negative scalar curvature, inspired by relativity models.

Contribution

It introduces a framework for warped products in Finsler geometry with scalar curvature conditions, extending classical Riemannian concepts to Finslerian settings.

Findings

Construction of warped product Finsler manifolds with prescribed scalar curvature.

Extension of classical warped product theory to Finsler metrics.

Application to models in relativity theory.

Abstract

The notion of warped product plays an important role in Riemannian geometry moreover in geodesic metric spaces. The warped product was first introduced by Bishop and O'Neill to study Riemannian manifolds of negative curvature.Warped products have been mainly used to construct new examples of Riemannian manifolds with prescribed curvature conditions. This construction can be extended for Finslerian metrics with some minor restrictions. This is motivated by Asanov's papers, where some models of relativity theory are described through the warped product of Finsler metrics. These metrics are in the form of $(\alpha,\beta)$-metrics, which are the generalization of the Randers metrics; which are being asymmetric Finsler metrics in four-dimensional space-time. The product was later extended to the warped product case of Finsler manifolds by the work of Kozma, Peter and Verge.