Higher rank 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=2(a)center dot 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.