Transcendental submanifolds of $\mathbb{R}{\mathbb{P}}^n$

Abstract

In this paper we give examples of closed smooth submanifolds of $\mathbb{R}{\mathbb{P}}^n$ which are isotopic to nonsingular projective subvarieties of $\mathbb{R}{\mathbb{P}}^n$ but they can not be isotopic to the real parts of nonsingular complex projective subvarieties of $\mathbb{C}{\mathbb{P}}^n$.