Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1990. Sectio Physicae (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 20)

Anatol Nowicki: Composite spacetime from twistors and its extensions

- 13 therefore we get the following reality condition: n

+Q + 0

+n = 0 C8b) or using the notation C7a) we have three relations: rt o + o a l 0 a i n* (o

0

2 + O*"

1^ = 0 C8c) a 2 rt o + o "

a

i = 0 at where n* = Ci^*, O*

0^ = Co^)* and * denotes the complex 'aß conjugation. In the twistor framework the equations C8c) say that the twistors T

±,T

2 are "null—twistors" with respect to the UC2,2) norm: CT

4,T

2> = CT

1,T

1) = CT

2,T

2) = O C9) where and CT,T} = t

+qt = («,- nf) J,] ( f

ß ) - [h ?] Therefore, the reality condition is equivalent to the zero condition for twistors i.e. to vanishing the UC2,2) norm of twistors T. The Z—plains generated by the "null twistors" are called totally null planes. In this way we obtain the following correspondence diagram: complex planes in TT < paints of CM* fcomplex^Minkowskil i I totally null planes <• —• points of KM* f

rea

l in TT ^ space J We would like to stress here, that from the point of view of the twistor theory, regaroling the relation C7c)

, it is more natural to use twistors for the description of the complex