Totally Real Minimal Tori in $CP^2$

Hui Ma; Yujie Ma

arxiv: math/0106141 · v1 · pith:JG43ZVNBnew · submitted 2001-06-17 · 🧮 math.DG · math-ph· math.MP

Totally Real Minimal Tori in CP²

Hui Ma , Yujie Ma This is my paper

classification 🧮 math.DG math-phmath.MP

keywords omegatoriequationminimalrealtotallytzitzeicacorrespond

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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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Totally Real Minimal Tori in CP²

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