Warped embeddings between Einstein manifolds

TL;DR

This paper analyzes warped embeddings of Einstein manifolds, providing explicit solutions for various codimensions and discussing their features and potential applications.

Contribution

It offers explicit solutions for warped embeddings of Einstein manifolds across different codimensions, expanding understanding of their geometric properties.

Findings

Explicit embedding metrics for codimension 1 cases

Partial solutions for higher codimension embeddings

Discussion of features and potential applications

Abstract

Warped embeddings from a lower dimensional Einstein manifold into a higher dimensional one are analyzed. Explicit solutions for the embedding metrics are obtained for all cases of codimension 1 embeddings and some of the codimension n>1 cases. Some of the interesting features of the embedding metrics are pointed out and potential applications of the embeddings are discussed.