Submanifolds in five-dimensional pseudo-Euclidean spaces and four-dimensional FRW universes

TL;DR

This paper derives equations for embedding four-dimensional FRW universes into five-dimensional pseudo-Euclidean spaces, providing a general framework and specific examples to understand their geometric properties.

Contribution

It presents a general formulation of embedding equations for FRW universes in five-dimensional pseudo-Euclidean spaces, including explicit examples.

Findings

Derived general equations for submanifolds in pseudo-Euclidean spaces.

Provided specific examples of embeddings of FRW universes.

Enhanced understanding of geometric structures of cosmological models.

Abstract

Equations for submanifolds, which correspond to embeddings of the four-dimensional FRW universes in five-dimensional pseudo-Euclidean spaces, are presented in convenient form in general case. Several specific examples are considered.