An immersed $S^{n}$ $\lambda$-hypersurface

TL;DR

This paper constructs a new example of an immersed, non-embedded $ ext{S}^n$ $ ext{lambda}$-hypersurface in Euclidean space, expanding the known types of such geometric objects.

Contribution

It introduces the first known immersed, non-embedded $ ext{S}^n$ $ ext{lambda}$-hypersurface in Euclidean space, providing new insights into their geometric properties.

Findings

Existence of immersed, non-embedded $ ext{S}^n$ $ ext{lambda}$-hypersurfaces

Construction method for such hypersurfaces

Extension of known classifications of $ ext{lambda}$-hypersurfaces

Abstract

In this paper, we construct an immersed, non-embedded $S^{n}$ $\lambda$-hypersurface in Euclidean spaces $\mathbb{R}^{n+1}$.