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Calabi lifting and surface geometry in \(S^ 4\). (English) Zbl 0613.53025

To an isometric immersion of an orientable surface M into \(S^ 4(1)\), there correspond two maps \(M\to P_ 3({\mathbb{C}})\), which are called Calabi liftings, where \(P_ 3({\mathbb{C}})\) is considered as the twistor space of \(S^ 4(1)\). The author studies some relations between an isometric immersion into \(S^ 4(1)\) and its Calabi liftings. He proves among others that Calabi liftings of an orientable minimal surface in \(S^ 4(1)\) are conformal minimal immersions into \(P_ 3({\mathbb{C}})\).
Reviewer: K.Ogiue

MSC:

53C40 Global submanifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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