Euclidean hypersurfaces with semi-parallel Moebius second fundamental form

TL;DR

This paper classifies a specific class of Euclidean hypersurfaces with semi-parallel Moebius second fundamental form and three distinct principal curvatures, completing a broader classification effort in differential geometry.

Contribution

It provides a complete classification of umbilic-free Euclidean hypersurfaces with semi-parallel Moebius second fundamental form and three principal curvatures, extending previous work.

Findings

Classification of such hypersurfaces completed

Identification of geometric properties of these hypersurfaces

Extension of prior classification results

Abstract

In this paper, we classify Euclidean umbilic-free hypersurfaces with semi-parallel Moebius second fundamental form and three distinct principal curvatures. This completes the classification of such hypersurfaces initiated by Hu, Xie and Zhai in the article: Submanifolds with semi-parallel Mobius second fundamental form in the unit sphere. J.Geom. Anal. 33 (2023), 44pp.