Higher rank homogeneous Clifford structures

Details Higher rank homogeneous Clifford structures Higher rank homogeneous Clifford structures

2011-10-19

arxiv.org/abs/1110.4260v1

Mathematics

Differential Geometry

20 pages

Scientific paper

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 $r=2^a\cdot b$ with $b$ odd, then $r\le 9$ for $a=0$, $r\le 10$ for $a=1$, $r\le 12$ for $a=2$ and $r\le 16$ for $a\ge 3$. Moreover, we describe the four limiting cases and show that there is exactly one solution in each case.

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