Advances in Applied Clifford Algebras

, Volume 13, Issue 2, pp 231–240 | Cite as

The twistor structure of the biquaternionic projective point

Original Paper


Souček [1, 2] discovered an intriguing connection between the standard twistor correspondence and the biquaternionic projective line \(\mathbb{B}\mathbb{P}^{1}. \) The biquaternionic projective point, \(\mathbb{B}\mathbb{P}^{0}, \) also has twistor structure corresponding to the collection of α- or β-planes passing through the origin in spacetime. The duality between α- or β-planes is shown to correspond to the choice of left vs. right scalar action. Moreover, we find that \(\mathbb{B}\mathbb{P}^{0} \) is homeomorphic to the scheme \(\mathbb{C}\mathbb{P}^{1}. \)


Projective Line Scalar Action Projective Point Popular Science Twistor Structure 


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Copyright information

© Birkhäuser Verlag, Basel 2003

Authors and Affiliations

  1. 1.Department of MathematicsCalifornia State University at FullertonFullertonU.S.A

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