ar X iv : m at h / 06 08 36 8 v 3 [ m at h . D G ] 2 7 Ju n 20 08 The Complex Structures on S 2 n
نویسنده
چکیده
In this paper, we show that the twistor space J (R2n+2) on Euclidean space R2n+2 is a Kaehler manifold and the orthogonal twistor space J̃ (S2n) of the sphere S2n is a Kaehler submanifold of J (R2n+2). Then we show that an orthogonal almost complex structure Jf on S 2n is integrable if and only if the corresponding section f : S2n → J̃ (S2n) is holomorphic. These shows there is no integrable orthogonal complex structure on the sphere S2n for n > 1.
منابع مشابه
ar X iv : m at h / 06 08 36 8 v 4 [ m at h . D G ] 2 8 Ju n 20 08 The Complex Structures on S 2 n
In this paper, we show that the twistor space J (R2n+2) on Euclidean space R2n+2 is a Kaehler manifold and the orthogonal twistor space J̃ (S2n) of the sphere S2n is a Kaehler submanifold of J (R2n+2). Then we show that an orthogonal almost complex structure Jf on S 2n is integrable if and only if the corresponding section f : S2n → J̃ (S2n) is holomorphic. These shows there is no integrable orth...
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