Regular Blaschke Para-Umbilical Hypersurfaces in the Conformal Space ${\mathbb Q}^n_s$

TL;DR

This paper classifies regular Blaschke para-umbilical hypersurfaces in conformal space, extending previous classifications of Blaschke quasi-umbilical submanifolds and conformal isotropic submanifolds.

Contribution

It provides a classification of Blaschke para-umbilical hypersurfaces in conformal space, expanding the understanding of submanifold geometry in this setting.

Findings

Classification of Blaschke para-umbilical hypersurfaces achieved

Extension of conformal isotropic submanifold classification

Advances in conformal submanifold theory

Abstract

In [2] we have classified the Blaschke quasi-umbilical submanifolds in the conformal space ${\mathbb Q}^n_s$. In this paper we shall classify the Blaschke para-umbilical hypersurfaces in the conformal space ${\mathbb Q}^n_s$. That may be also considered as the extension of the classification of the conformal isotropic submanifolds in the conformal space ${\mathbb Q}^n_s$.