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

The authors study the regular submanifolds in the conformal space ? _p ⁿ and introduce the submanifold theory in the conformal space ? _p ⁿ . The first variation formula of the Willmore volume functional of pseudo-Riemannian submanifolds in the conformal space ? _p ⁿ is given. Finally, the conformal isotropic submanifolds in the conformal space ? _p ⁿ are classified.