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The twistor structure of the biquaternionic projective point

Authors:	Email author" target="_blank">Alfonso?F?Agnew Email author

Institution:	(1) Department of Mathematics, California State University at Fullerton, Fullerton, CA, U.S.A

Abstract:	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 $\mathbb{C}\mathbb{P}^{1}.$

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