Classification of Codazzi and note on minimal hypersurfaces in $Nil^{4}$

TL;DR

This paper classifies Codazzi hypersurfaces and characterizes a specific class of minimal hypersurfaces in the four-dimensional Nil space, providing examples and insights into their geometric properties.

Contribution

It offers a new classification of Codazzi hypersurfaces and characterizes a particular class of minimal hypersurfaces in Nil^4, including explicit examples.

Findings

Classification of Codazzi hypersurfaces in Nil^4

Characterization of a class of minimal hypersurfaces in Nil^4

Explicit example of a minimal surface in this class

Abstract

In this paper, we give a classification of Codazzi hypersurfaces in a Lie group $(Nil^{4},\widetilde g)$. We also give a characterization of a class of minimal hypersurfaces in $(Nil^{4},\widetilde g)$ with an example of a minimal surface in this class.