The supersymmetric components of the Riemann–Einstein tensor as nine dimensional spheres in ten dimensional space

In eight dimensional superspace, the number of independent components of the Riemann–Einstein tensor is R(8) = 336. The paper shows that these components could be given a geometrical interpretation as a hyperbolic tesselation via the (k = 11 − 4 = 7) modular group Γ(7). In addition the components may be viewed as 336 particles-like states resembling 9-dimensional spheres in 10 dimensional space. Finally a relation to the 528 killing vector fields in 32 dimensional super and maximally symmetric space related to 11 dimensional P-Branes with 528 = (336)(11/7) states is established.