Geodesic rigidity of conformal connections on surfaces
Geodesic rigidity of conformal connections on surfaces
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表面上共形连接的测地刚度
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
T. Mettler
中科院分区：
文献类型：
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作者：
T. Mettler
我们表明，一个共形连接的封闭导向表面$$Sigma $的负欧拉特征保持正是一个共形结构，而且是唯一确定的非参数化测地线。作为推论，$$Sigma $$Σ上的Riemannian度量的未参数化测地线确定了直到常数重新标度的度量。它还表明，每一个共形连接上的$$2-球面在于一个复杂的$5-流形的共形连接，所有这些共享相同的非参数测地线。
We show that a conformal connection on a closed oriented surface $$Sigma $$Σ of negative Euler characteristic preserves precisely one conformal structure and is furthermore uniquely determined by its unparametrised geodesics. As a corollary it follows that the unparametrised geodesics of a Riemannian metric on $$Sigma $$Σ determine the metric up to constant rescaling. It is also shown that every conformal connection on the $$2$$2-sphere lies in a complex $$5$$5-manifold of conformal connections, all of which share the same unparametrised geodesics.