Riemann Extension of the Anti-Mach Space time

TL;DR

This paper derives the Riemann extension of the anti-Mach spacetime, analyzes its geodesic equations, studies its properties, and constructs a translation surface in four dimensions, expanding understanding of this geometric structure.

Contribution

It introduces the Riemann extension of the anti-Mach metric and explores its properties and geodesic solutions, providing new insights into its geometric structure.

Findings

Riemann extension of the anti-Mach metric is derived.

Geodesic equations for the extended space are solved.

A translation surface in four dimensions is constructed.

Abstract

Riemann extension for the anti Mach metric is derived, the solution of geodesic equations for the extended space are given, some properties for the extended space was studied and compared with the basic space and the constructions of a translation surface for the anti Mach metric in four dimension is established.