H-hypersurfaces with at most 3 distinct principal curvatures in the Euclidean spaces

TL;DR

This paper classifies H-hypersurfaces in Euclidean spaces with up to three distinct principal curvatures, providing theoretical results and explicit examples for these geometric structures.

Contribution

It offers a complete classification of H-hypersurfaces with three distinct curvatures in Euclidean spaces, expanding understanding of their geometric properties.

Findings

Complete classification of H-hypersurfaces with three principal curvatures

Derived new results on H-hypersurfaces in Euclidean spaces

Constructed explicit examples of such hypersurfaces

Abstract

In this paper, we study hypersurfaces of Euclidean spaces with arbitrary dimension. First, we obtain some results on $\mbox{H}$-hypersurfaces. Then, we give the complete classification of $\mbox{H}$-hypersurfaces with 3 distinct curvatures. We also give explicit examples.