153 
own. It is an invariant with eventually possible deformations of the 
Vy in. the. Ze | \ 
The quantity on the left is the curvature of the V,, tangent to 
the V,, in P and geodesie in this point, in particular thus of the 
V built up by the geodesic lines of the V, tangent to the V,, in 
P. We call this quantity the forced curvature K. of the Vin: 
kK, = ah (48) 
The last term with negative sign is the curvature of the V,,, if 
the linear element of the V,, were euclidean, or the relative curvature 
te the 1: 
2 
Ke ft She ~'hy (eh ii. (44) 
m (ml) 
Hence we have the theorem: 
The absolute curvature of a Vm im Vy is an invariant of defor- 
mation and equal to the sum of the relative and the forced curvature. 
When the JV, is an S,, we have 
K. } 6 4 Kk K 
Sn 2 eM RK 45 
(Gh) if nn S ( ) 
consequently K- is independent of the situation and the linear element 
of the V,,. Hence in this case K‚ is also an invariant of deformation. 
In the general case K, is an day apt oe deformation in P for all 
Reaal of the Vas with, which 3 ‘K is an invariant, thus in 
particular for the deformations with which the m-direction, of the 
Vn in:P remains unaltered. 
The relative curvature of the V,, with respect to the Fa built 
up by a direction i, continued in some way in the J,, i 
2 
ee ST apa tet st 2 (la — 'he) (he EE 'he) . (46) 
m (m— 1) 
We thus have: | 
= = re é ; (47) 
in words: 
hr we pass through a V in an arbitrary way n—m mutual 
ET” perpendicular Vini the relatwe curvature of the Vn with 
HeeVoss; SO Lope sd: 
i %) The names absolute and relative curvature are introduced by Ricci, 02, 1, 
p. 361. 
