  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 ${\mathbb Q}^n_p$.
