Regular Submanifolds in the Conformal Space ${\mathbb Q}^n_p$

TL;DR

This paper develops a general theory of regular submanifolds in the conformal space ${ m Q}^n_p$, including the first variation formula of the Willmore volume functional and classification of conformal isotropic submanifolds.

Contribution

It introduces a comprehensive submanifold theory in ${ m Q}^n_p$, deriving the first variation formula for the Willmore functional and classifying conformal isotropic submanifolds.

Findings

Derived the first variation formula of the Willmore volume functional.

Constructed a general submanifold theory in ${ m Q}^n_p$.

Classified conformal isotropic submanifolds.

Abstract

There is a Lorenzian group acting on the conformal space ${\mathbb Q}^n_p$. We study the regular submanifolds in the conformal space ${\mathbb Q}^n_p$ and construct general submanifold theory in the conformal space ${\mathbb Q}^n_p$. Finally we give the first variation formula of the Willmore volume functional of submanifolds in the conformal space ${\mathbb Q}^n_p$ and classify the conformal isotropic submanifolds in the conformal space ${\mathbb Q}^n_p$.