Ejiri, Norio Calabi lifting and surface geometry in \(S^ 4\). (English) Zbl 0613.53025 Tokyo J. Math. 9, 297-324 (1986). 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 Cited in 1 ReviewCited in 5 Documents MSC: 53C40 Global submanifolds 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) Keywords:isometric immersion; Calabi liftings; twistor space; minimal surface PDFBibTeX XMLCite \textit{N. Ejiri}, Tokyo J. Math. 9, 297--324 (1986; Zbl 0613.53025) Full Text: DOI