( 123 ) 



when choosing that point as centre of' a system of Rie^iann normal 

 coordinates 



( 



i. e. a system such that as = — 



^'" = -(0-^ + 5? + a 



but as V^ of a vector distribution with components A^, Y and Z, 

 we tlnd for the .I'-component X^i: 



/ d'X d'X d'X^ 



^ V ÖA-^ ^'f ^^'' 



The hyperbolic Sp^. 



I. As first derivative Y of a vector distribution X we find a 

 planivector determined bj a scalar value: 



1 j a(X,^) a(A,^)j 



As second deri\-ative Z we find the scalar : 

 1 j d(X,^) ^{X,A) ] 



II. If X is to be a ^X, i. e. a second derivative of a planivector 

 with scalar value ip we must have : 



Bdv AÖU 



to which end is necessary and sufficient : ^= 0. 



If 



have 



If A' is to be a qX, i.e. a first derivative of a scalar ^ we must 





A^u ' '' Bbv 



to which end is necessary and sufficient: F=3 0. 



III. The oA', of which the divergency is an isolated scalar value 

 in the origin, becomes a vector distribution in the direction of the 

 radius vector: 



1 



sinh r 

 It is the first derivative of a scalar dislribntion 



I colli A r. 



