A class of Einstein submanifolds of Euclidean space

TL;DR

This paper classifies a specific class of Einstein submanifolds within Euclidean space, focusing on both local and global properties, especially emphasizing codimension two cases with intrinsic assumptions.

Contribution

It provides new local and global parametric classifications of Einstein submanifolds, particularly in codimension two, based solely on intrinsic geometric assumptions.

Findings

Classification of Einstein submanifolds in Euclidean space

Explicit parametrizations for codimension two cases

Intrinsic assumptions suffice for classification

Abstract

In this paper we give local and global parametric classifications of a class of Einstein submanifolds of Euclidean space. The highlight is for submanifolds of codimension two since in this case our assumptions are only of intrinsic nature.