10-Dim Einstein spaces made up on basis of 6-Dim Ricci-flat spaces and 4-Dim Einstein spaces

TL;DR

This paper constructs ten-dimensional vacuum Einstein spaces using four- and six-dimensional Ricci-flat spaces derived from solutions of the Sin-Gordon equation, and discusses their geodesic properties.

Contribution

It introduces a method to build 10D Einstein spaces from lower-dimensional Ricci-flat spaces linked to Sin-Gordon solutions, expanding geometric modeling techniques.

Findings

Examples of 10D vacuum Einstein spaces are constructed.

Geodesic properties of these spaces are analyzed.

Connections to Sin-Gordon equation solutions are established.

Abstract

Some examples of ten-dimensional vacuum Einstein spaces made up on basis of four-dimensional Ricci-flat spaces and six-dimensional Ricci-flat spaces defined by solutions of the Sin-Gordon equation are constructed. The properties of geodesics for such type of the spaces are discussed