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- W50536825 abstract "It is well known that 6-dimensional standard sphere S has a nearly Kahler structure(see [KN], pp139-140). We denote by J the nearly Kahler structure. It is an interesting problem to classify J-invariant submanifolds of S. Due to a result of A. Gray[Gr], there is no 4-dimensional J-invariant submanifolds. Thus, the only possibility of J-invariant submanifold is the case of the image of Riemann surface by some immersion, which we call an almost comples curve(or J-holomorphic curve). Let φ : S −→ S be an almost complex curve. If φ is linearly full and the ellipses of curvature and the second curvature are circles, then φ is said to be superminimal. On the other hand, Bolton-VranckenWoodward([BVW]) proved that if φ is linearly full in some totally geodesic S in S then m = 2, 5 or 6. This, together with a general result on superminimal surfaces by Calabi([Ca]), means that almost complex curves are divided into the following four types : (I) linearly full in S and superminimal, (II) linearly full in S and non-superminimal, (III) linearly full in some totally geodesic S in S (necessarily non-superminimal)," @default.
- W50536825 created "2016-06-24" @default.
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- W50536825 date "2002-03-01" @default.
- W50536825 modified "2023-09-24" @default.
- W50536825 title "Almost Complex Curves of Type(III) in the Nearly Kahler 6-Sphere" @default.
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