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