Homogeneous Clifford structures

Abstract

We give an upper bound for the rank r of homogeneous (even) Clifford structures on compact manifolds of non-vanishing Euler characteristic. More precisely, we show that if
r = 2a � b with b odd, then r � 9 for a = 0, r � 10 for a = 1, r � 12 for a = 2 and r � 16
for a � 3. Moreover, we describe the four limiting cases and show that there is exactly one solution in each case.