Totally Real Minimal Tori in $C{P}^2$

Abstract

In this paper we show that all totally real superconformal minimal tori in $C{P}^2$ correspond with doubly-periodic finite gap solutions of the Tzitzeica equation $${\omega }_{z\overline{z}}=e^{-2\omega }-e^{\omega }$$ Using the results on the Tzitzeica equation in integrable system theory, we describe explicitly all these tori by Prym-theta functions.

22 pages

Cited by in corpus (3)

• Lectures on Calabi-Yau and special Lagrangian geometry
• Lectures on special Lagrangian geometry
• Hamiltonian stationary tori in the complex projective plane