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Twistor analysis of a parabola

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GTAW01 - General relativity: from geometry to amplitudes

The Penrose twistor space CP3 can be used to parametrize orthogonal complex structures on domains of R4. In particular, a complex quadric Q defines a natural complex structure on R4 minus a line. Quaternionic power series can then be lifted to holomorphic maps from Q to CP3. Applying this to a quadratic polynomial allows one to understand the elementary geometry associated to a parabola and the circular cones in 3-dimensional space that contain it.

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