We give a condition for a function to produce a Möbius invariant weighted inner product on the tangent space of the space of knots, and show that some kind of Möbius invariant knot energies can produce Möbius invariant and parametrization invariant weighted inner products. They would give a natural way to study the evolution of knots in the framework of Möbius geometry.

中文翻译：

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节点空间的莫比乌斯不变度量

我们给出了一个函数在结空间的切空间上产生莫比乌斯不变加权内积的条件，并证明某种莫比乌斯不变结能量可以产生莫比乌斯不变和参数化不变加权内积。他们将提供一种自然的方法来研究莫比乌斯几何框架中节点的演化。