Embedding of the Brane into Six Dimensions

TL;DR

This paper presents a geometric embedding of a brane into a six-dimensional Euclidean space, visualizing its structure as a hyper-sphere surface influenced by the cosmological constant, linking brane geometry with higher-dimensional space.

Contribution

It introduces a novel embedding of the brane metric into a six-dimensional Euclidean space, providing a geometric visualization of brane structure related to the cosmological constant.

Findings

Brane geometry modeled as a hyper-sphere surface in six dimensions.

Minkowski space represented as an intersection with the hyper-sphere surface.

Embedding offers new insights into brane structure in higher-dimensional space.

Abstract

Embedding of the brane metric into Euclidean (2+4)-space is found. Brane geometry can be visualized as the surface of the hyper-sphere in six dimensions which 'radius' is governed by the cosmological constant. Minkowski space in this picture is lied on the intersection of this surface with the plane formed by the extra space-like and time-like coordinates.