We prove LeBrun–Salamon conjecture in the following situation: if X is a contact Fano manifold of dimension \(2n+1\) whose group of automorphisms is reductive of rank \(\ge \max (2,(n-3)/2)\) then X is the adjoint variety of a simple group. The rank assumption is fulfilled not only by the three series of classical linear groups but also by almost all the exceptional ones.

中文翻译：

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接触歧管上的高级圆环作用

我们在以下情况下证明LeBrun-Salamon猜想：如果X是维\（2n + 1 \）的接触Fano流形，其自同构群是秩\（\ ge \ max（2，（n-3）/ 2）\），那么X是一个简单组的伴随变体。等级假设不仅可以通过三组经典线性组来满足，而且可以通过几乎所有例外组来满足。