$\delta$(3)-ideal null 2-type hypersurfaces in Euclidean spaces

TL;DR

This paper classifies $ ext{delta}(3)$-ideal null 2-type hypersurfaces in Euclidean spaces, showing they must have constant mean and scalar curvature, advancing understanding of finite type submanifolds.

Contribution

It proves that all $ ext{delta}(3)$-ideal null 2-type hypersurfaces in Euclidean spaces have constant mean and scalar curvature, providing a key classification result.

Findings

Null 2-type hypersurfaces are the simplest beyond 1-type.

All $ ext{delta}(3)$-ideal null 2-type hypersurfaces have constant mean curvature.

All such hypersurfaces have constant scalar curvature.

Abstract

In the theory of finite type submanifolds, null 2-type submanifolds are the most simple ones, besides 1-type submanifolds (cf. e.g., [3, 12]). In particular, the classification problems of null 2-type hypersurfaces are quite interesting and of fundamentally important. In this paper, we prove that every $\delta$(3)-ideal null 2-type hypersurface in a Euclidean space has constant mean curvature and constant scalar curvature.