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

preprint2011arXivOpen access

Abstract

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

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