We study homogenous Weyl connections with non-positive sectional curvatures.The Cartesian product $\mathbb S^1 \times M$ carries canonical families of Weylconnections with such a property, for any Riemmanian manifold $M$. We provethat if a homogenous Weyl connection on a manifold, modeled on a unimodular Liegroup, is non-positive in a stronger sense (streched non-positive), then itmust be locally of the product type.
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机译：我们研究具有非正截面曲率的同质Weyl连接。笛卡尔乘积$ \ mathbb S ^ 1 \ times M $对于任何Riemmanian流形$ M $都具有具有这种性质的Weylconnection规范族。我们证明，如果以单模李群为模型的流形上的同质Weyl连接在更强的意义上是非正的（拉长的非正），则它必须是产品类型的局部。
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