Totally Real Minimal Tori in $CP^2$

Details Totally Real Minimal Tori in $CP^2$ Totally Real Minimal Tori in $CP^2$

2001-06-17

arxiv.org/abs/math/0106141v1

Mathematics

Differential Geometry

22 pages

Scientific paper

In this paper we show that all totally real superconformal minimal tori in $CP^2$ 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.

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