Coordinate-free study of Finsler spaces of $H_{p}$-scalar curvature

TL;DR

This paper provides an intrinsic, coordinate-free analysis of special Finsler spaces with $H_{p}$-scalar curvature, characterizations, and conditions relating to scalar and constant curvature, supported by examples.

Contribution

It introduces an intrinsic approach to study $H_{p}$-scalar curvature in Finsler spaces, including characterizations and conditions for curvature properties, with new examples.

Findings

Characterization of Finsler spaces with $H_{p}$-scalar curvature

Conditions for $H_{p}$-scalar curvature to imply perpendicular scalar curvature

Criteria for scalar curvature spaces to have $H_{p}$-constant curvature

Abstract

The aim of the present paper is to provide an \emph{intrinsic} investigation of special Finsler spaces of $H_{p}$-scalar curvature and of $H_{p}\,$-constant curvature. Characterizations of such spaces are shown. Sufficient condition for Finsler space of $H_{p}$-scalar curvature to be of perpendicular scalar curvature is investigated. Necessary and sufficient condition under which a Finsler space of scalar curvature turns into a Finsler space of $H_{p}$-scalar curvature is given. Further, certain conditions under which a Finsler manifolds of $H_{p}$-scalar curvature and of scalar curvature reduce to a Finsler manifold of $H_{p}$-constant curvature are obtained. Finally, various examples are studied and constructed.