NDLI: The twistor theory of the Hermitian Hurwitz pair (ℂ4(I 2,2),ℝ(I 2,3))

Content Provider	Springer Nature Link
Author	⌊ódź, Julian Ławrywicz Tokyo, Osamu Suzuki
Copyright Year	1998
Abstract	An analogue of the twistor theory is given for the Hermitian Hurwitz pair(ℂ4(I 2,2),ℝ(I 2,3)). In Sect. 2 a concept of Hurwitz twistors is introduced and a counterpart of the Penrose correspondence is obtained. It is proved that there exists a one-to-one correspondence between the twistors on the (1,3)-space and the (2,2)-space, which is called the duality theorem for Hurwitz twistors (Theorem 1). In Sect. 3. a concept of spinor equations is introduced for an Hermitian Hurwitz pair (abbreviated as HHP) and the duality theorem for solutions of the spinor equations is proved (Theorem 2). In Sect. 4 we give an elementary proof of the Penrose theory on the base of our Key Lemma. Then we can give the desired correspondence explicitly. In sect. 5 we consider the Penrose theory in the context of HHPs. At first we give a local version. It is proved that every solution of the spinor equation on the (2,2)-space can be represented as a ∂-harmonic one-form. By use of this result, we can get a direct relationship between the complex analysis and spinor theory on some open setM +, which is called as “semi-global version” of the Penrose theory (Theorem 7). Moreover, we can get the original Penrose theory by use of the Penrose transformation (Theorem 5).
Ending Page	179
Page Count	33
Starting Page	147
File Format	PDF
ISSN	01887009
e-ISSN	16614909
Journal	Advances in Applied Clifford Algebras
Issue Number	1
Volume Number	8
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	1998-01-01
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	space with an indefinite scalar product Twistor theory, double fibrations Mathematical Methods in Physics Mathematical and Computational Physics Clifford analysis Hurwitz pair twistor Applications of Mathematics Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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