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

Abstract

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

arXiv comment20 pages