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- W2066528048 abstract "In this paper almost complex surfaces of the nearly Kahler $S^3times S^3$ are studied in a systematic way. We show that on such a surface it is possible to define a global holomorphic differential, which is induced by an almost product structure on the nearly Kahler $S^3times S^3$. We also find a correspondence between almost complex surfaces in the nearly Kahler $S^3times S^3$ and solutions of the general $H$-system equation introduced by Wente, thus obtaining a geometric interpretation of solutions of the general $H$-system equation. From this we deduce a correspondence between constant mean curvature surfaces in $mathbb R^3$ and almost complex surfaces in the nearly Kahler $S^3times S^3$ with vanishing holomorphic differential. This correspondence allows us to obtain a classification of the totally geodesic almost complex surfaces. Moreover, we will prove that almost complex topological 2-spheres in $S^3times S^3$ are totally geodesic. Finally, we also show that every almost complex surface with parallel second fundamental form is totally geodesic." @default.
- W2066528048 created "2016-06-24" @default.
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- W2066528048 date "2012-08-03" @default.
- W2066528048 modified "2023-09-27" @default.
- W2066528048 title "Almost complex surfaces in the nearly Kahler $S^3times S^3$" @default.
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